Multiple solutions to boundary value problems for semilinear elliptic equations
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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.
CitationLuyen, D. T., & Tri, N. M. (2021). Multiple solutions to boundary value problems for semilinear elliptic equations. Electronic Journal of Differential Equations, 2021(48), pp. 1-12.
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