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INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

机译:具有指数临界增长的外域中的不确定拟线性椭圆型方程

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摘要

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.
机译:本文关注拟线性问题的解是否存在{-div(vertical bar del u垂直bar(N-2)del u)+垂直bar u垂直bar(N-2)u = a(x)g( u)在Omega中对于偏导数Omega,u = 0,其中R(N)(N> = 2)的Omega子集是外部域;也就是说,Omega = R(N) omega,其中R(N)的omega子集是有界域,非线性g(u)在无穷大处具有指数临界增长,而a(x)是连续函数并改变符号在欧米茄。应用变分方法来建立上述问题的非平凡解的存在。

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