Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2000-04-01

Journal: ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals: CSCD、SCIE、Scopus

Volume: 16

Issue: 2

Page Number: 349-360

ISSN: 1000-9574

Key Words: elliptic boundary value problems; Leray-Schauder degree continuation method; Landesman-Lazer condition; semi-Landesman-Lazer conditions; sign condition

Abstract: In this paper we prove a very general result concerning solvability of the resonant problem: Delta u + lambda(k) u + g(x, u) = h(x) u = 0, x is an element of partial derivative Omega, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when lambda(k) = lambda(1), in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.