The variational analysis of a nonlinear anisotropic problem with no-flux boundary condition

چکیده مقاله

We study the nonlinear degenerate anisotropic problem (Formula presented.),where Ω⊂R^N is a bounded domain with smooth boundary. The constant value of the boundary data is not specified, whereas the zero integral term corresponds to a no-flux boundary condition. In the case when |u|^q(x)-2u “dominates” the left-hand side, we show that a nontrivial solution exists for all positive values of λ. If the term |u|^q(x)-2u is dominated by the left-hand side, we prove that a solution exists either for small or for large values of $$\lambda >0$$λ>0. The proofs combine variational arguments with energy estimates. © 2014, Springer-Verlag Italia.