Sign-changing solutions for non-local elliptic equations
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Date
2017-07-14
Authors
Luo, Huxiao
Journal Title
Journal ISSN
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. Electronic Journal of Differential Equations, 2017(180), pp. 1-15.
Rights
Attribution 4.0 International