On the Fredholm-type theorems and sign properties of solutions for (p, q)-Laplace equations with two parameters

Abstract

We consider the Dirichlet problem for the nonhomogeneous equation - Δ pu- Δ qu= α| u| p-2u+ β| u| q-2u+ f(x) in a bounded domain, where p≠ q, and α, β∈ R are parameters. We explore assumptions on α and β that guarantee the resolvability of the considered problem. Moreover, we introduce several curves on the (α, β) -plane allocating sets of parameters for which the problem has or does not have positive or sign-changing solutions, provided f is of a constant sign.