On an elliptic Kirchhoff-Boussinesq type problems with exponential growth

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.