On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

• Autorzy: Wenjie Gao , Junyu Wang
• Języki publikacji: EN

Abstrakty

EN

The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

Słowa kluczowe

EN

two-point boundary value problems; upper and lower solutions; Nagumo condition; existence; Carathéodory functions

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems
• 34B10: Nonlocal and multipoint boundary value problems
• 34C25: Periodic solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 3
• Strony: 283-291

Daty

wydano

1995

otrzymano

1994-11-20

Twórcy

autor

Wenjie Gao

• Department of Mathematics, Jilin University, Changchun 130023, P.R. China

autor

Junyu Wang

• Department of Mathematics, Jilin University, Changchun 130023, P.R. China

Bibliografia

• [1] A. Adje, Sur et sous-solutions généralisées et problèmes aux limites du second ordre, Bull. Soc. Math. Belgique Sér. B 42 (1990), 347-368.
• [2] J. Bebernes, A simple alternative problem for finding periodic solutions of second order ordinary differential systems, Proc. Amer. Math. Soc. 42 (1974), 121-127.
• [3] A. Cabada and J. J. Nieto, A generalization of the monotone iterative technique for nonlinear second-order periodic boundary value problems, J. Math. Anal. Appl. 151 (1990), 181-189.
• [4] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111-128.
• [5] M.-X. Wang, A. Cabada and J. J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993), 221-235.