Borysenko, Sergiy and Gallo, Angela and Piccirillo, Anna Maria (2010) Multidimensional Impulse Inequalities and General Bihari-Type Inequalities for Discontinuous Functions with Retardation. (Sottomesso)
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| Tipologia del documento: | Preprint |
|---|---|
| Titolo: | Multidimensional Impulse Inequalities and General Bihari-Type Inequalities for Discontinuous Functions with Retardation |
| Autori: | Autore Email Borysenko, Sergiy [non definito] Gallo, Angela [non definito] Piccirillo, Anna Maria [non definito] |
| Data: | 2010 |
| Dipartimento: | Matematica e applicazioni "Renato Caccioppoli" |
| Sezione di dipartimento: | INGEGNERIA |
| Data: | 2010 |
| Riferimenti bibliografici: | [ 1 ] R.P.Agarwal,On an integral inequality in n-independent variables. J.Math. Anal. Appl. 85 (1982), pp.192-196. [ 2 ] R.P.Agarwal,Difference Equations and Inequalities: Theory, Methods and Applications, New York.1992. [ 3 ] O. Akinyele, On Gronwall-Bellman-Bihari type integral inequalities in several variables with retardation, J.Math.Anal.Appl. 104 (1) (1984) ,pp.1-26 . 4 N.V. Azbelev, Z.B.Tsalyuk,On Chaplygin’s problem, Ukrain. Mat. Zh. 10 (1) (1958), pp.3-12 . 5 D.Bainov,P.S.Simeonov, Integral Inequalities and Applications, Kluwer Acad. Pubbl., Dordreht,1992. 6 R.Bellman,K.L.Cooke, Differential – Difference equations, Academic Press, New York,1963. [ 7 ] I.Bihari, A generalization of lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math.Acad.Scient.Hung. 7(1)(1956) 71-94. [8 ] D.S.Borysenko, About the integral inequality for piecewise continuous functions,in:Proc.X Int.Kravchuk Conf.,Kyiv 2004,p.323 [ 9 ] D.S.Borysenko, A.Gallo, R.Toscano, Integral inequalities Gronwall-Bellman type for discontinuous functions, Visnik Kyiv University (1) (2005) 63-67. [10] D.S.Borysenko, A.Gallo, R.Toscano, Integral inequalities Gronwall-Bellman type for discontinuous functions and estimates of solutions impulsive systems, in: Proc.DE@CAS, Brest,2005,pp.5-9. [11] S.D.Borysenko, Integro-sum inequalities for functions of many independent variables, Differential equations, 25 (9) (1989) ,pp.1638-1641. [12] S.D.Borysenko, G.Iovane, P.Giordano, Investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces, Nonlinear Anal. 62(2005), pp. 345-363. [13] S.D.Borysenko,M.Ciarletta, G.Iovane, Integro-sum inequalities and motion stability of systems with impulse perturbations, Nonlinear Anal. 62(2005) 417-428. [14] S.D.Borysenko, G.Iovane, P.Giordano,About some hyperbolic impulsive equations and estimate solutions,in:Proc.DE@CAS,Brest,2005, pp.9-14. [15] S.D.Borysenko,G.Iovane,Integro-Sum Inequalities and Qualitative Analysis Dinamical Systems with Perturbations, Tipografia-Legatoria “ELDA” Università of Salerno, Salerno, 2006. [16] S.D.Borysenko,G.Iovane,Integro-Sum Inequalities and Qualitative Analysis Dinamical Systems withPerturbations, Tipografia-Legatoria “ELDA” Università of Salerno, Salerno, 2006. [17 ] S.D.Borysenko, G.Iovane, About some integral inequalities of Wendroff type for discontinuous functiolns. Nonlinear Anal. 66(10) 2007 ,pp.2190-2203 . [ 18 ] A.Gallo, A.M. Piccirillo,About new analogies Gronwall – Bellman – Bihari type inequalities for discontinuous functions and estimates solutions impulsive differential systems, Nonlinear Anal.67(2007) 5, pp.1550-1559. [19] G.Iovane,S.D.Borysenko,Boundedness,stability, practical stability of motion impulsive systems,in:Proc.DE@CAS,Brest,2005,pp.15-21. [20] G.Iovane, Some new integral inequalities of Bellman Bihari type with delay for discontinuous functions, Nonl.Anal. 66 (2007), pp. 498-508. [21] S.C. Hu, V.Lakshmikantham, S.Leela, Impulsive differential systems and the pulse phenomena, J.Math. Anal. Appl. 137 (2) (1989) 605-612. [22] V.Lakshmikantham, S.Leela, Differential and Integral Inequalities, Theory and Applications, Academic Press, New York, 1969. [23]V.Lakshmikantham, S.Leela, M.Mohan Rao Rama, Integral and integro-differential inequalities, Appl. Anal. 24(3)(1987) 157-164. [24] V.Lakshmikantham, D.Bainov, P.S.Simeonov, Theory of Impulsive Differential Equation, Ser.Modern Appl. Math. 6, 1989. [25] A.A. Martyhyuk, V.Lakshmikantham, S.Leela, Stability of Motion: the Method of Integral Inequalikties, Naukova Dumka, Kyiv, 1989. [26] Yu.A.Mitropolskiy, S.Leela, A.A. Martyhyuk,About some derections of investigations of V.Lakshmikantham in theory of differential equations and applications, Differ.Uravn. 22 (4) (1986) 550-572. [27]Yu.A.Mitropolskiy, G. Iovane, S.D. Borysenko, About a generalization of Bellman- Bihari type inequalities for discontinuous functions and their applications. Nonlinear Anal. 66(2007) (10), pp.2140-2165. 28 J.J. Nieto, Basic theory for nonresonance impulsive periodic problems of first order, J.Math.Anal.Appl., 1997 (205) , pp. 423-433. 29 J.J. Nieto, Impulsive resonance periodic problems of first order, Appl. Math. Letters, 2002 /15), pp. 489- 493. [30] B.G. Pachpatte, On some integral inequalities similar to Bellman-Bihari inequality, J. Math. Anal. Appl. 49 (1975) 794-802. [31] B.G. Pachpatte, On some new integral and integrodifferential inequalities in two independent variables and their applications. J. Differential Equations 33 (1979), pp.249- 272. [32] B.G. Pachpatte, On some new integro-differential inequalities of the Wendroff type. J.Math. Anal. Appl. 73 (1980), pp.491-500. 33A.M. Piccirillo, Estimates of the solutions hyperbolic equations with impulse perturbations, in: Proc. XI Int. Kravchuk Conf. Kyiv, 2006,pp.77-80. 34A.M. Piccirillo, I. Verigina, About some generalization Bihari result for integro-sum inequalities, in: Proc. XI Int. Kravchuk Conf. Kyiv, 2006,p. 187. 35 L.F. Rakhmatullina, On some application of stability conditions of Chaplyging problems for the problems of boundedness and solution stability of differential equations. Izv. Vuzov, 2(1959), pp. 198-201. 36 A.M.Samoilenko, S.D.Borysenko, C.Cattani, G.Matarazzo, V.Visinsky, Differential Models: Stability, Inequalities and Estimates, Naukova Dumka, Kyiv, 2001. [37] A.M.Samoilenko,N. Perestyuk, Differential Equations with Impulse Effect, Visha Shkola, Kyiv, 1987. (1977) 423-432 . [38] E.Thahdapani, R.D. Agarwal, On some new inequalities in n-indipendent variables, J. Math. Anal. Appl. 86 (1982), pp.542-561. [39] C.G. Yeh, Wendroff inequalitity in n-indipendent variables, J. Math. Anal. Appl.78 (1980), pp. 78-87. [40] C.G. Yeh, M.H. Shih, The Gronwall- Bellman inequality in several variables, J.Math.Anal. Appl. 86 (1982), pp.157-167. [41] W. Walter, Differential and Integral Inequalities, Springer- Verlag, New York, 1970. [42] Z.B. Tsalyuk, Multidimensional integral inequalities, Differents Uravneniya ,(1983) (10), pp. 1828-1839. •••••••••• [ 1 ] R.P.Agarwal,On an integral inequality in n-independent variables. J.Math. Anal. Appl. 85 (1982), pp.192-196. [ 2 ] R.P.Agarwal,Difference Equations and Inequalities: Theory, Methods and Applications, New York.1992. [ 3 ] O. Akinyele, On Gronwall-Bellman-Bihari type integral inequalities in several variables with retardation, J.Math.Anal.Appl. 104 (1) (1984) ,pp.1-26 . 4 N.V. Azbelev, Z.B.Tsalyuk,On Chaplygin’s problem, Ukrain. Mat. Zh. 10 (1) (1958), pp.3-12 . 5 D.Bainov,P.S.Simeonov, Integral Inequalities and Applications, Kluwer Acad. Pubbl., Dordreht,1992. 6 R.Bellman,K.L.Cooke, Differential – Difference equations, Academic Press, New York,1963. [ 7 ] I.Bihari, A generalization of lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math.Acad.Scient.Hung. 7(1)(1956) 71-94. [8 ] D.S.Borysenko, About the integral inequality for piecewise continuous functions,in:Proc.X Int.Kravchuk Conf.,Kyiv 2004,p.323 [ 9 ] D.S.Borysenko, A.Gallo, R.Toscano, Integral inequalities Gronwall-Bellman type for discontinuous functions, Visnik Kyiv University (1) (2005) 63-67. [10] D.S.Borysenko, A.Gallo, R.Toscano, Integral inequalities Gronwall-Bellman type for discontinuous functions and estimates of solutions impulsive systems, in: Proc.DE@CAS, Brest,2005,pp.5-9. [11] S.D.Borysenko, Integro-sum inequalities for functions of many independent variables, Differential equations, 25 (9) (1989) ,pp.1638-1641. [12] S.D.Borysenko, G.Iovane, P.Giordano, Investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces, Nonlinear Anal. 62(2005), pp. 345-363. [13] S.D.Borysenko,M.Ciarletta, G.Iovane, Integro-sum inequalities and motion stability of systems with impulse perturbations, Nonlinear Anal. 62(2005) 417-428. [14] S.D.Borysenko, G.Iovane, P.Giordano,About some hyperbolic impulsive equations and estimate solutions,in:Proc.DE@CAS,Brest,2005, pp.9-14. [15] S.D.Borysenko,G.Iovane,Integro-Sum Inequalities and Qualitative Analysis Dinamical Systems with Perturbations, Tipografia-Legatoria “ELDA” Università of Salerno, Salerno, 2006. [16] S.D.Borysenko,G.Iovane,Integro-Sum Inequalities and Qualitative Analysis Dinamical Systems withPerturbations, Tipografia-Legatoria “ELDA” Università of Salerno, Salerno, 2006. [17 ] S.D.Borysenko, G.Iovane, About some integral inequalities of Wendroff type for discontinuous functiolns. Nonlinear Anal. 66(10) 2007 ,pp.2190-2203 . [ 18 ] A.Gallo, A.M. Piccirillo,About new analogies Gronwall – Bellman – Bihari type inequalities for discontinuous functions and estimates solutions impulsive differential systems, Nonlinear Anal.67(2007) 5, pp.1550-1559. [19] G.Iovane,S.D.Borysenko,Boundedness,stability, practical stability of motion impulsive systems,in:Proc.DE@CAS,Brest,2005,pp.15-21. [20] G.Iovane, Some new integral inequalities of Bellman Bihari type with delay for discontinuous functions, Nonl.Anal. 66 (2007), pp. 498-508. [21] S.C. Hu, V.Lakshmikantham, S.Leela, Impulsive differential systems and the pulse phenomena, J.Math. Anal. Appl. 137 (2) (1989) 605-612. [22] V.Lakshmikantham, S.Leela, Differential and Integral Inequalities, Theory and Applications, Academic Press, New York, 1969. [23]V.Lakshmikantham, S.Leela, M.Mohan Rao Rama, Integral and integro-differential inequalities, Appl. Anal. 24(3)(1987) 157-164. [24] V.Lakshmikantham, D.Bainov, P.S.Simeonov, Theory of Impulsive Differential Equation, Ser.Modern Appl. Math. 6, 1989. [25] A.A. Martyhyuk, V.Lakshmikantham, S.Leela, Stability of Motion: the Method of Integral Inequalikties, Naukova Dumka, Kyiv, 1989. [26] Yu.A.Mitropolskiy, S.Leela, A.A. Martyhyuk,About some derections of investigations of V.Lakshmikantham in theory of differential equations and applications, Differ.Uravn. 22 (4) (1986) 550-572. [27]Yu.A.Mitropolskiy, G. Iovane, S.D. Borysenko, About a generalization of Bellman- Bihari type inequalities for discontinuous functions and their applications. Nonlinear Anal. 66(2007) (10), pp.2140-2165. 28 J.J. Nieto, Basic theory for nonresonance impulsive periodic problems of first order, J.Math.Anal.Appl., 1997 (205) , pp. 423-433. 29 J.J. Nieto, Impulsive resonance periodic problems of first order, Appl. Math. Letters, 2002 /15), pp. 489- 493. [30] B.G. Pachpatte, On some integral inequalities similar to Bellman-Bihari inequality, J. Math. Anal. Appl. 49 (1975) 794-802. [31] B.G. Pachpatte, On some new integral and integrodifferential inequalities in two independent variables and their applications. J. Differential Equations 33 (1979), pp.249- 272. [32] B.G. Pachpatte, On some new integro-differential inequalities of the Wendroff type. J.Math. Anal. Appl. 73 (1980), pp.491-500. 33A.M. Piccirillo, Estimates of the solutions hyperbolic equations with impulse perturbations, in: Proc. XI Int. Kravchuk Conf. Kyiv, 2006,pp.77-80. 34A.M. Piccirillo, I. Verigina, About some generalization Bihari result for integro-sum inequalities, in: Proc. XI Int. Kravchuk Conf. Kyiv, 2006,p. 187. 35 L.F. Rakhmatullina, On some application of stability conditions of Chaplyging problems for the problems of boundedness and solution stability of differential equations. Izv. Vuzov, 2(1959), pp. 198-201. 36 A.M.Samoilenko, S.D.Borysenko, C.Cattani, G.Matarazzo, V.Visinsky, Differential Models: Stability, Inequalities and Estimates, Naukova Dumka, Kyiv, 2001. [37] A.M.Samoilenko,N. Perestyuk, Differential Equations with Impulse Effect, Visha Shkola, Kyiv, 1987. (1977) 423-432 . [38] E.Thahdapani, R.D. Agarwal, On some new inequalities in n-indipendent variables, J. Math. Anal. Appl. 86 (1982), pp.542-561. [39] C.G. Yeh, Wendroff inequalitity in n-indipendent variables, J. Math. Anal. Appl.78 (1980), pp. 78-87. [40] C.G. Yeh, M.H. Shih, The Gronwall- Bellman inequality in several variables, J.Math.Anal. Appl. 86 (1982), pp.157-167. [41] W. Walter, Differential and Integral Inequalities, Springer- Verlag, New York, 1970. [42] Z.B. Tsalyuk, Multidimensional integral inequalities, Differents Uravneniya ,(1983) (10), pp. 1828-1839. •••••••••• |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Depositato il: | 29 Giu 2011 09:15 |
| Ultima modifica: | 30 Apr 2014 19:46 |
| URI: | http://www.fedoa.unina.it/id/eprint/8458 |
Abstract
In this article we investigate some impulsive integro-functional inequalities for functions of n independent variables. The problem of reducing multidimensional integro-sum functional inequalities to one-dimensional inequalities is considered too (by using conditions of solvability Chapligin’ problem for impulsive integral inequalities). Some new analogies Wendroff-type inequalities for discontinuous functions with finite jumps are founded.
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