论文标题

在$ \ r^n $中的Ambrosetti-Prodi类型问题上

On an Ambrosetti-Prodi type problem in $\R^N$

论文作者

Alves, Claudianor O., de Lima, Romildo N., Nóbrega, Alânnio B.

论文摘要

在本文中,我们研究了以下Ambrosetti-prodi类型问题的存在和不存在的结果,$$ \ left \ left \ {\ begin {array} {lcl} {lcl}-ΔU= p(x)\ big(g big(g(u) d^{1,2}(\ r^n),\ \ lim_ {| x | \ to +\ infty} u(x)= 0,\ end {array} \ right。 \ eqno {(p)} $$其中$ n \ geq3 $,$ p \ in C(\ r^n,\ r^+)$,$ f \ in C(\ r^n)\ cap l^{\ infty}(\ r^infty}(\ r^n)$ and c^in c^in c^1(\ r)$。所使用的主要工具是子启动方法和Leray-Schauder拓扑学位理论。

In this paper we study results of existence and non-existence of solutions for the following Ambrosetti-Prodi type problem $$ \left\{ \begin{array}{lcl} -Δu=P(x)\Big( g(u)+f(x)\Big) \mbox{ in } \mathbb{R}^N,\\ u \in D^{1,2}(\R^N),\ \lim_{|x|\to +\infty}u(x)=0, \end{array} \right. \eqno{(P)} $$ where $N\geq3$, $P\in C(\R^N,\R^+)$, $f\in C(\R^N)\cap L^{\infty}(\R^N)$ and $g\in C^1(\R)$. The main tools used are the sub-supersolution method and Leray-Schauder topological degree theory.

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