Multiple solutions of some nonlinear strongly resonant elliptic equations without the (PS) condition
The author proves several lower bounds for the number of distinct pairs of solutions to the nonlinear resonance problem \(- \Delta u = f(x,u)\) in \(\Omega\), \(u = 0\) on \(\partial \Omega\), where \(f(x,s) = \lambda_ks + p(x,s)\), and \(\lambda_k\) is an eigenvalue of the Laplacian with homogeneous Dirichlet condition.
semilinear elliptic problem of resonance
scientific article; zbMATH DE number 811196