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

Vladimir Bobkov, Mieko Tanaka

We consider the Dirichlet problem for the nonhomogeneous equation $-{\Delta }_{p}u-{\Delta }_{q}u=\alpha |u{|}^{p-2}u+\beta |u{|}^{q-2}u+f(x)$ in a bounded domain, where $p\ne q$, and $\alpha ,\beta \in \mathbb{R}$…