Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Abstract

It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (Φ 1 , Φ 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities combined with indefinite potentials and singular cases perturbed by superlinear and subcritical couple terms. These prevent us to use arguments based on Ambrosetti-Rabinowitz condition and variational methods for differentiable functionals. By exploring the Nehari method and doing a fine analysis on the fibering map associated, we get estimates that allow us unify the arguments to show multiplicity of semi-trivial solutions in both cases.

Some recent results on singular $ p $-Laplacian systems

“…Sufficient conditions for the existence of sub-super-solution pairs to (12) are given in [27,. As an example, via Theorem 3.4 one can show that the model problem (cf.…”

“…As far as we know, till today, much less attention has been paid to multiplicity of solutions. Actually, we can only mention the papers [68,12,26,5,49]. The first deals with singular p(x)-Laplacian systems while the second is devoted to quasilinear problems driven by (Φ 1 , Φ 2 )-Laplace operators.…”

Some recent results on singular p-laplacian systems

“…As far as we know, till today, much less attention has been paid to multiplicity of solutions. Actually, we can only mention the papers [67,12,26,5,50]. The first deals with singular p(x)-Laplacian systems while the second is devoted to quasi-linear problems driven by (Φ 1 , Φ 2 )-Laplace operators.…”