Unbounded nonlinear perturbations of linear elliptic problems at resonance

DOI オープンアクセス

この論文をさがす

説明

435 where lj is an eigenvalue of L, a/& is the derivative in the direction outward normal to the boundary &2 of 0, and f~ H-“(Q). Recently, Shapiro [lo] established an existence result for the problem (1.1) in the case that g has unbounded nonlinearities and satisfies a Landesman-Lazer type condition. Shapiro’s result, however, does not cover the case that g has linear growths. Our first result is an extension of Shapiro’s result to the case that g has a linear growth. We next consider the case g does not satisfies any Landesman-Lazer type condition. That is, we study the case lim inf, _ oc g(x, t) = lim supI _ up g(x, t), a.e. on Q. Several authors considered this case with g having bounded nonlinearities (cf. [9]). Fucik and Krebec [5] and Hess [6] gave existence results for (1.1) in case that j?‘~ L”(Q) and g is a continuous function satisfying g(x, t) = g(t), g(-t)=g(r), and g+ =lim,+ fm g(t) = 0. We extend these results for (1.1) to the case g has unbounded nonlinearities and f~ L2. Our method employed here is different from those in [S, 6, or lo]. 2.

収録刊行物

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ