Elliptic and Parabolic Equations - Abstract

Kyritsi, Sophia

Nonlinear elliptic equations with singularities

We consider a singular parametric elliptic equation driven by the $p$-Laplacian and with a $p$-superlinear potential which does not satisfy the Ambrosetti--Rabinowitz condition. Using variational arguments, combined with truncation techniques and the method of upper and lower solutions, we show that there exists a $lambda^*$ such that if the parameter $lambda$ is in $(0,lambda^*)$, then the problem has two ordered smooth positive strong solutions.