On the superlinear problems involving the fractional Laplacian

Bin Ge; Chao Zhang

doi:10.1007/s13398-015-0236-4

On the superlinear problems involving the fractional Laplacian

Bin Ge^*
, Chao Zhang

^*Corresponding author for this work

School of Mathematics

Harbin Engineering University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we consider a kind of nonlinear eigenvalue problem involving the fractional Laplacian without Ambrosetti–Rabinowitz condition, that is, (Formula presented.), where Ω⊂ R^N is a bounded smooth domain, α∈ (0 , 1) , (- Δ) ^α stands for the fractional Laplacian, λ> 0 is a parameter, and f(x, u) is superlinear at infinity. Existence of nontrivial solutions is established for arbitrary λ> 0.

Original language	English
Pages (from-to)	343-355
Number of pages	13
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	110
Issue number	2
DOIs	https://doi.org/10.1007/s13398-015-0236-4
State	Published - 1 Sep 2016

Keywords

Critical points
Eigenvalue problem
Fractional-Laplacian
Superlinear
Variational method

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10.1007/s13398-015-0236-4

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keywords = "Critical points, Eigenvalue problem, Fractional-Laplacian, Superlinear, Variational method",

author = "Bin Ge and Chao Zhang",

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KW - Critical points

KW - Eigenvalue problem

KW - Fractional-Laplacian

KW - Superlinear

KW - Variational method

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JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

IS - 2

ER -

On the superlinear problems involving the fractional Laplacian

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Keywords

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