Document Type : Research Paper

Authors

• Abdolrahman Razani
• Farzaneh Safari

Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

Abstract

Here, the existence of at least one nontrivial solution for the $(p,q)$-Laplacian problem
\[
\left\{ \begin{array}{lc}
div(|\nabla u|^{p-2}\nabla u)+div(|\nabla u|^{q-2}\nabla u)=f(x,u)\qquad &  x\in \Omega, \\
\\
|\nabla u|^{p-2}\frac{\partial u}{\partial n}+ |\nabla u|^{q-2}\frac{\partial u}{\partial n}=g(x,u)  & x\in  \partial  \Omega
\end{array} \right.
\]
is done, where $ \Omega$ is a bounded domain in $\mathbb{R}^N, N\geq 3$ and $q, p\geq 2$, via variational methods.

Keywords

• $(p
• q)$-Laplace equation
• Steklov boundary conditions
• Mountain Pass Theorem