Abstract
In this paper, we prove the existence and multiplicity of solutions for a fractional Kirchhoff equation involving a sign-changing weight function which generalizes the corresponding result of Tsung-fang Wu (Rocky Mt. J. Math. 39:995-1011, 2009). Our main results are based on the method of a Nehari manifold.
Highlights
In this paper, we consider the following fractional elliptic equation with sign-changing weight functions: ⎧ ⎨M( R N|u(x)–u(y)|p |x–y|N +sp dx dy)(–)spu = λf (x)uq + g(x)ur, x∈⎩u =, x ∈ RN \, ( . )
We may assume that the weight functions f (x) and g(x) are as follows: (H ) f + = max{f, } ≡, and f ∈ Lμq (
⎩u =, x ∈ RN \, and they obtained the multiplicity of non-negative solutions in the subcritical case α < p∗s by minimizing the energy functional over non-empty decompositions of Nehari manifold
Summary
1 Introduction In this paper, we consider the following fractional elliptic equation with sign-changing weight functions: We may assume that the weight functions f (x) and g(x) are as follows: (H ) f + = max{f , } ≡ , and f ∈ Lμq ( ⎩u = , x ∈ RN \ , and they obtained the multiplicity of non-negative solutions in the subcritical case α < p∗s by minimizing the energy functional over non-empty decompositions of Nehari manifold.
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