Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem
Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem
In this paper, we prove the existence and multiplicity of solutions for the following Robin problem \begin{equation*} \left\{ \begin{array}{cc} -\text{div}\left( a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u\right) =\lambda b(x)\left\vert u\right\vert ^{q(x)-2}, & x\in \Omega \\ a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+\beta (x)\left\vert u\right\vert ^{p(x)-2}u=0, & x\in \partial \Omega ,% \end{array}% \right. …