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Indexed by:期刊论文

Date of Publication:2000-04-01

Journal:ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals:Scopus、SCIE、CSCD

Volume:16

Issue:2

Page Number:349-360

ISSN No.: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.