On the solvability of a Neumann boundary value problem at resonance

Canadian mathematical bulletin

关键词: Landesman-Lazer condition;    Leray Schauder degree;   

DOI  :  10.4153/CMB-1997-055-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We study the existence of solutions of the semilinear equations (1)$riangle u + g(x,u)=h$, ${partial u over partial n} = 0$ on$partial Omega$ in which the non-linearity $g$ may growsuperlinearly in $u$ in one of directions $u o infty$ and $u o-infty$, and (2) $-riangle u + g(x,u)=h$, ${partial u overpartial n} = 0$ on $partial Omega$ in which the nonlinear term $g$may grow superlinearly in $u$ as $|u| o infty$. The purpose of thispaper is to obtain solvability theorems for (1) and (2) when theLandesman-Lazer condition does not hold. More precisely, we requirethat $h$ may satisfy $int g^delta_- (x) , dx < int h(x) , dx = 0

【 授权许可】

Unknown