Abstract
In this paper, the existence of a pair of ordered solutions for the following class of equations in (1) was studied. A bounded (PS) (Palais-Smale) sequence was constructed and the related variational principle was used to prove the existence of the positive solution. The existence of the ordered solutions is finally found.
Highlights
In recent years, studies about the nontrivial solutions of Schrödinger equations are very popular, involving differential equations, linear algebra and many subjects
A bounded (PS) (Palais-Smale) sequence was constructed and the related variational principle was used to prove the existence of the positive solution
We observe that formally problem (2) is the Euler-Lagrange equation associated of the natural energy functional given by
Summary
Studies about the nontrivial solutions of Schrödinger equations are very popular, involving differential equations, linear algebra and many subjects. The solution of these problems cannot only develop new methods, such as minimizations [1] [2], change of variables [3] [4] [5], Nehari method [6] and perturbation method [7], reveal new laws, and have important academic value and wide application prospects [8] [9]. We consider the existence of ordered solutions for the following quasilinear Schrödinger equations:. (g7) There exists μ ≥ 4 , such that 0 < μG ( x, s) < g ( x, s) s for any s > 0
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