Multiplicity of positive solutions for a degenerate nonlocal problem with p-Laplacian

We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the Lq-norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of "positive bumps"of the degenerate term. The solutions are also ordered according to their Lq-norms

Parametric nonlinear resonant Robin problems

We consider a nonlinear Robin problem driven by the ▫$p$▫-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly ▫$(p-1)$▫-sublinear and the other one is ▫$(p-1)$▫-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter ▫$lambda$▫ the problem has at least five nontrivial smooth solutions

Multiple solutions for asymptotically (p-1)-homogeneous p-Laplacian equations

AbstractWe consider a nonlinear elliptic equation driven by the p-Laplacian and with a reaction term which exhibits a (p−1)-homogeneous growth both near ±∞ and near zero. Using critical point theory with truncation techniques, the method of upper–lower solutions and Morse theory, we show that the problem has five nontrivial smooth solutions, four of which have constant sign (two positive and two negative)