Abstract
In this paper, we obtain one positive solution and two nontrivial solutions of a quasilinear elliptic equation with p-Laplacian, Hardy term and Hardy-Sobolev critical exponent by using variational methods and some analysis techniques. In particular, our results extend some existing ones.
Highlights
Introduction and main resultsWe shall study the following quasilinear elliptic equation: pu μ |u|p– |x|p u =|u|p∗ (s)– |x|s u + f (x, u), x∈\ { }, u =, x ∈ ∂, ( . )where pu = div(|∇u|p– ∇u) denotes the p-Laplacian differential operator, is an open bounded domain in RN (N ≥ ) with smooth boundary ∂ and ∈, ≤ μ < μ :=
We extend the special case p = in [ ] to a more general situation < p < N
We prove Theorems . and . by critical point theory
Summary
For some special f and p = , some authors ([ – ], s = ) ([ , – ], s = ) have studied the existence of solutions for Ding and Tang [ ] obtained the existence and multiplicity of solutions for The author [ ] obtained one positive solution for a special case of The corresponding energy functional fails to satisfy the classical Palais-Smale ((PS) for short) condition in W ,p( ).
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