Sign-changing solutions for non-local elliptic equations

Date

2017-07-14

Authors

Luo, Huxiao

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the existence of sign-changing solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions, -LKu = ƒ(x, u), x ∈ Ω, u = 0, x ∈ ℝn \ Ω, where Ω ⊂ ℝn (n ≥ 2) is a bounded, smooth domain and the nonlinear term ƒ satisfies suitable growth assumptions. By using Brouwer's degree theory and Deformation Lemma and arguing as in [2], we prove that there exists a least energy sign-changing solution. Our results generalize and improve some results obtained in [27].

Description

Keywords

Brouwer's degree theory, Sign-changing solutions, Non-local elliptic equations, Deformation Lemma

Citation

Luo, H. (2017). Sign-changing solutions for non-local elliptic equations. <i>Electronic Journal of Differential Equations, 2017</i>(180), pp. 1-15.

Rights

Attribution 4.0 International

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