Existence of solutions for a class of quasilinear elliptic equations in R^N with vanishing potentials

Abstract

Using variational methods, we establish the existence of positive solutions for a class of quasilinear elliptic problem

where Δ _p u = div(|∇u| ^p−2∇u) with 1 < p < N, f : R → R is continuous having a subcritical growth and V is a nonnegative potential, which can vanish at infinity, that is, V(∞) → 0 as |x| → ∞, or shortly, V(∞) = 0.

Keywords:

• quasilinear elliptic equation
• positive solution
• existence
• vanishing potentials

AMS Subject Classifications::

• 35J65
• 35J50

Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 11171092) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 08KJB110005).