A weak solution for a (p(x), q(x))-Laplacian elliptic problem with a singular term

Here, we consider the following elliptic problem with variable components: -a(x)Delta(p(x))u - b(x)Delta(q(x))u + u vertical bar u vertical bar(s-2)/vertical bar x vertical bar(s) = lambda f(x,u), with Dirichlet boundary condition in a bounded domain in RN with a smooth boundary. By applying the variational method, we prove the existence of at least one nontrivial weak solution to the problem.

Automated summary

By applying the variational method, the existence of at least one nontrivial weak solution to an elliptic problem with variable components is proven.