School of Mathematical Sciences
Dalian University of Technology
116024 Dalian, China
email: 22401008@mail.dlut.edu.cn
School of Mathematical Sciences
Dalian University of Technology
116024 Dalian, China
email: fangxd0401@dlut.edu.cn
Xuan Long, Xiang-Dong Fang
Abstract:
This article concerns the existence of solutions to the generalized quasilinear Schrodinger equation
$$
-\text{div} (g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u), \quad
x\in \mathbb{R}^N,
$$
where \(N \ge 1\), \(g \in C^1(\mathbb{R})\) and the nonlinearity is asymptotically linear at infinity.
Through the stretching transformation, we adjust the approach in [1]
and overcome the impediment that there might not exist a \(t>0\) such that \(t u_\infty(x-y)\)
belongs to the Nahari manifold, where \(u_\infty\) is a ground state solution for the limiting problem.
Submitted January 5, 2026. Published February 26, 2026.
Math Subject Classifications: 35J20, 35J62, 49J35.
Key Words: Quasilinear Schrodinger equation; asymptotically linear; Nehari manifold.
DOI: 10.58997/ejde.2026.19
Show me the PDF file (424 KB), TEX file for this article.
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Xuan Long School of Mathematical Sciences Dalian University of Technology 116024 Dalian, China email: 22401008@mail.dlut.edu.cn |
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Xiang-Dong Fang School of Mathematical Sciences Dalian University of Technology 116024 Dalian, China email: fangxd0401@dlut.edu.cn |
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