Existence Results to Elliptic Problems With Dirichlet Boundary Condition Involving a P-Harmonic Operator

Abstract

In this note, we prove the existence of a non-trivial weak solution for a nonlinear equation involving a p-harmonic operator through a local minimization theorem, under Dirichlet boundary value conditions. In the case of terms with a sublinear growth near the origin, we ensure the existence of solutions for small positive values of the parameter. Moreover, the corresponding solutions have smaller energies as the parameter goes to zero.