Multiple solutions of degenerate perturbed elliptic problems involving a subcritical Sobolev exponent
The authors study the degenerate elliptic equation \[ -\text{div}(a(x)\nabla u)+ b(x)u=K(x) |u|^{p-2}u +g(x) \quad \text{in} \mathbb{R}^N, \] where \(N\geq 2\) and \(2<p<2N/(N-2).\) Under suitable assumptions on the functions \(a,\) \(b\), and \(K\) it is proved that if the perturbation \(g\) is sufficiently small than the above problem has at least two distinct solutions in an appropriate weighted Sobolev space.
scientific article; zbMATH DE number 1545377