Sign-charging solutions for \(p\)-Laplacian equations with jumping nonlinearity and the Fučik spectrum
The authors prove existence of sign-changing solutions to the \(p\)-Laplace type equation \[ -\Delta_pu+\lambda g(x)|u|^{p-2}u=f(u)\quad x\in \mathbb{R}^N, \] with a positive parameter \(\lambda\) and a right-hand side \(f(u)\) exhibiting jumping nonlinearities at infinity which is superlinear at \(u=0.\) The proof relies on the Fučik spectrum and the authors give sufficient conditions ensuring its existence.
scientific article; zbMATH DE number 6700553