Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity

Abstract

By an application of Bonanno's three critical point theorem, we establish the existence of a nontrivial solution to the problem $$displaylines{ -Delta_p u= mu frac{g(x)|u|^{p-2}u}{|x|^p} +lambda a(x)f(u) quad hbox{in }Omega,cr u =0quad hbox{on }partial Omega, }$$ under some restrictions on g,a and f for certain positive values of $mu$ and $lambda$.

Keywords

• p-Laplacian
• singularity
• multiple solutions