On an elliptic Kirchhoff-Boussinesq type problems with exponential growth

被引:7
作者
Carlos, Romulo D. [1 ]
Figueiredo, Giovany M. [1 ,2 ]
机构
[1] Univ Brasilia UnB, Dept Matemat, Brasilia, Brazil
[2] Univ Brasilia UnB, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
关键词
biharmonic operator; critical exponential growth; p-Laplacian; BIHARMONIC EQUATION; P-LAPLACIAN; NONTRIVIAL SOLUTIONS; EXISTENCE;
D O I
10.1002/mma.9662
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we prove an existence result of nontrivial solutions for the problem & UDelta;2u & PLUSMN;& UDelta;pu=f(u)in & omega;,andu=& UDelta;u=0on partial differential & omega;,$$ {\Delta} circumflex 2u\pm {\Delta}_pu equal to f(u)\kern0.20em \mathrm{in}\kern0.20em \Omega, \mathrm{and}\kern0.20em u equal to \Delta u equal to 0\kern0.5em \mathrm{on}\kern0.20em \mathrm{\partial \Omega }, $$where & omega;& SUB;Double-struck capital R4$$ \Omega \subset {\mathrm{\mathbb{R}}} circumflex 4 $$ is a smooth bounded domain, 2<p<4$$ 2<p<4 $$ and f:Double-struck capital R & RARR;Double-struck capital R$$ f:\mathrm{\mathbb{R}}\to \mathrm{\mathbb{R}} $$ is a superlinear continuous function with exponential subcritical or critical growth. We apply the Nehari manifold method in order to prove the main result.
引用
收藏
页码:397 / 408
页数:12
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