본문 바로가기
KERD
논문KCI 등재

On Opial Type Inequalities with Nonlocal Conditions and Applications

3

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

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)

  1. P. R. Beesack, "On an integral inequality of Z. Opial", Trans. Amer. math. Soc, 104 (1962)
  2. R. C. Brown, "An Opial-type inequality with an integral boundary con-dition", Proc. R. Soc. Lond. Ser. A, 461, pp.2635~2651 (2005)
  3. R. C. Brown, "Opial's inequality and oscillation of 2nd order equa-tions", Proc. Amer. math. Soc, 125(4), pp.1123~1129 (1997)
  4. J. Calvert, "Some generalizations of Opial's inequality", Proc. Amer. math. Soc, 18, pp.72~75 (1967)
  5. K. M. Das, "An inequality similar to Opials inequality", Proc. Amer. math. Soc, 22, pp.258~261 (1969)
  6. B. J. Harris, "On the oscillation of differential equations with an oscilla-tory coefficient", Trans. Amer. math. Soc, 347, pp.1831~1839 (1995)
  7. M. K. Kwong, "On an Opial inequality with a boundary condition", J. Ineq. Pure Appl.Math, 8(1), pp.4~ (2007)
  8. D. S. Mitrinovic, "Inequalities involving functions and their derivatives", Kluwer Academic Publishers
  9. C. Olech, "A simple proof of a certain result of Z. Opial", Ann. Polon. Math, 8, pp.61~63 (1960)
  10. Z. Opail, "Sur une inegalité", Ann. Polon. Math, 8, pp.29~32 (1960)
  11. G. S. Yang, "On a certain result of Z. Opial", Proc. Japan Acad, 42, pp.78~83 (1966)

관련 논문AI추천

이 간행물의 다른 논문 (9건)