A generalized periodic boundary value problem for the one-dimensional p-Laplacian

• Autorzy: Daqing Jiang , Junyu Wang
• Języki publikacji: EN

Abstrakty

EN

The generalized periodic boundary value problem -[g(u')]' = f(t,u,u'), a < t < b, with u(a) = ξu(b) + c and u'(b) = ηu'(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, $g(s) = |s|^{p-2} s$, p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.

Słowa kluczowe

EN

generalized periodic boundary value problem; p-Laplacian; upper and lower solutions; Carathéodory function; Nagumo condition

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 3
• Strony: 265-270

Daty

wydano

1997

otrzymano

1996-06-05

Twórcy

autor

Daqing Jiang

• Department of Mathematics, Northeast Normal University, Changchun 130024, P.R. China

autor

Junyu Wang

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

Bibliografia

• [1] W. J. Gao and J. Y. Wang, On a nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 62 (1995), 283-291.
• [2] J. Y. Wang, W. J. Gao and Z. H. Lin, Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem, Tôhoku Math. J. 47 (1995), 327-344.
• [3] 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.