Multiple solutions to boundary value problems for semilinear elliptic equations
Date
2021-05-28
Authors
Luyen, Duong
Tri, Nguyen Minh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the multiplicity of weak solutions to the boundary value problem
-Δu = ƒ(x, u) + g(x, u) in Ω,
u = 0 on ∂Ω,
where Ω is a bounded domain with smooth boundary in ℝN (N > 2), ƒ(x, ξ) is odd in ξ and g is a perturbation term. Under some growth conditions on ƒ and g, we show that there are infinitely many solutions. Here we do not require that ƒ be continuous or satisfy the Ambrosetti-Rabinowitz (AR) condition. The conditions assumed here are not implied by the ones in [3, 15]. We use the perturbation method Rabinowitz combined with estimating the asymptotic behavior of eigenvalues for Schrödinger's equation.
Description
Keywords
Semilinear elliptic equations, Multiple solutions, Critical points, Perturbation methods, Boundary value problem
Citation
Luyen, D. T., & Tri, N. M. (2021). Multiple solutions to boundary value problems for semilinear elliptic equations. <i>Electronic Journal of Differential Equations, 2021</i>(48), pp. 1-12.
Rights
Attribution 4.0 International