Duong Trong Luyen, Nguyen Minh Tri
In this article, we study the multiplicity of weak solutions to the boundary value problem
where Ω is a bounded domain with smooth boundary in RN (N > 2), f(x,ξ) is odd in ξ and g is a perturbation term. Under some growth conditions on f and g, we show that there are infinitely many solutions. Here we do not require that f 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 by Rabinowitz combined with estimating the asymptotic behavior of eigenvalues for Schrödinger's equations.
Submitted September 18, 2019. Published May 28, 2021.
Math Subject Classifications: 35J60, 35B33, 35J25, 35J70.
Key Words: Semilinear elliptic equations; multiple solutions; critical points; perturbation methods; boundary value problem.
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| Duong Trong Luyen |
Division of Computational Mathematics and Engineering
Institute for Computational Science, and
Faculty of Mathematics and Statistics
Ton Duc Thang University, Ho Chi Minh City, Vietnam
| Nguyen Minh Tri |
Institute of Mathematics
Vietnam Academy of Science and Technology
18 Hoang Quoc Viet
10307 Cau Giay, Hanoi, Vietnam
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