一类拟线性薛定谔方程解的存在性
Existence of Solutions for a Class of Quasilinear Schrödinger Equations
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摘要: 研究了一类拟线性薛定谔方程解的存在性问题,在位势强制下,当非线性项在原点处超线性,在无穷远处渐近三次时,利用山路引理,得到了该问题的一个非平凡解.Abstract: The existence of solutions for a class of quasilinear Schrödinger equations with coercive potential is investigated. By using the mountain pass lemma, a nontrivial solution is obtained when the nonlinear term is asymptotically linear at the origin and asymptotically triple at infinity.