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On Opial Type Inequalities with Nonlocal Conditions and Applications
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The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.
Abstract
The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.
참고문헌 (11)
- P. R. Beesack, "On an integral inequality of Z. Opial", Trans. Amer. math. Soc, 104 (1962)
- R. C. Brown, "An Opial-type inequality with an integral boundary con-dition", Proc. R. Soc. Lond. Ser. A, 461, pp.2635~2651 (2005)
- R. C. Brown, "Opial's inequality and oscillation of 2nd order equa-tions", Proc. Amer. math. Soc, 125(4), pp.1123~1129 (1997)
- J. Calvert, "Some generalizations of Opial's inequality", Proc. Amer. math. Soc, 18, pp.72~75 (1967)
- K. M. Das, "An inequality similar to Opials inequality", Proc. Amer. math. Soc, 22, pp.258~261 (1969)
- B. J. Harris, "On the oscillation of differential equations with an oscilla-tory coefficient", Trans. Amer. math. Soc, 347, pp.1831~1839 (1995)
- M. K. Kwong, "On an Opial inequality with a boundary condition", J. Ineq. Pure Appl.Math, 8(1), pp.4~ (2007)
- D. S. Mitrinovic, "Inequalities involving functions and their derivatives", Kluwer Academic Publishers
- C. Olech, "A simple proof of a certain result of Z. Opial", Ann. Polon. Math, 8, pp.61~63 (1960)
- Z. Opail, "Sur une inegalité", Ann. Polon. Math, 8, pp.29~32 (1960)
- G. S. Yang, "On a certain result of Z. Opial", Proc. Japan Acad, 42, pp.78~83 (1966)
관련 논문AI추천
SOME OPIAL-TYPE INEQUALITIES APPLICABLE TO DIFFERENTIAL EQUATIONS INVOLVING IMPULSESYoung Jin Kim한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제4호New integral inequalities for nonlinear functions and their applicationsTae-In Kwon, Young-Ho Kim장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제1호A REFINEMENT OF LYAPUNOV-TYPE INEQUALITY FOR A CLASS OF NONLINEAR SYSTEMS김용인한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호ON OPIAL INEQUALITIES INVOLVING HIGHER ORDER DERIVATIVESChang-Jian Zhao, Wing-Sum Cheung대한수학회 · 대한수학회보2012 · 제49권 제6호On Opial-type inequalities via a new generalized integral operatorGhulam Farid, Yasir Mehboob강원경기수학회 · 한국수학논문집2021 · 제29권 제2호On weighted generalization of opial type inequalities in two variablesArtion Kashuri, Huseyin Budak, Mehmet Zeki Sarikaya강원경기수학회 · 한국수학논문집2020 · 제28권 제4호
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