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论文类型：期刊论文

发表时间：2000-04-01

发表刊物：ACTA MATHEMATICA SINICA-ENGLISH SERIES

收录刊物：Scopus、SCIE、CSCD

卷号：16

期号：2

页面范围：349-360

ISSN号：1000-9574

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

摘要：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.