In this paper, we study a nonlinear double phase problem with variable exponent and critical growth on the boundary. The has in reaction combined effects of Carathéodory perturbation defined only locally term. presence term does not permit to apply results point theory corresponding energy functional. Thus, use appropriate cut-off functions truncation techniques work an auxiliary coercive probl...

The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces variable exponent. existence uniqueness are treated by using penalty method reduction sense. also discuss nonexistence long-time behavior solutions.

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous p(x)- Laplacian equations, managed by non polynomial growth operator in framework variable exponent Sobolev spaces on Riemannian manifolds. mountain pass Theorem is used.