Weak Solutions and Energy Estimates for Singular p-Laplacian-Type Equations

摘要

This paper deals with the existence results and energy estimates of solutions for singular p-Laplacian-type equations if the nonlinear term admits some suitable conditions on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, we establish the existence of a non-zero solution and deduce the existence of solutions for positive values of the parameter, with requiring (p - 1)-sublinearity of nonlinear part at the origin and the infinity. Finally, a multiplicity result and two illustrating examples are also given. The proof is based on a local minimum theorem for differentiable functionals.