Luyen, DuongTri, Nguyen Minh2021-08-262021-08-262021-05-28Luyen, 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. 1-12.1072-6691https://hdl.handle.net/10877/14458In 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.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalSemilinear elliptic equationsMultiple solutionsCritical pointsPerturbation methodsBoundary value problemArticle