Abstract
This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstly study a new algorithm for finding the meromorphic solution for the mentioned equation via meromorphic inequalities presented in (Xu in J. Math. Study 38(1):71–86, 2015). Then we deal with the necessary and sufficient conditions of convergence and obtain the general solutions and the conditions of solvability for the mentioned equation by means of the meromorphic inequalities for the classical boundary value problems developed in (Guillot in J. Nonlinear Math. Phys. 25(3):497–508, 2018). These results generalize some previous results concerning the asymptotic behavior of solutions of non-delay systems of Schrödinger equations by applying the maximum principle approach with respect to the Schrödinger operator in (Wan in J. Inequal. Appl. 2017:104, 2017).
Highlights
Problem (1.1) is related to the existence of nontrivial meromorphic solutions for the following general Schrödinger equations (see [2, 12, 20] for more details):
1 Introduction This article is devoted to the study of the general Schrödinger equation with general superlinear nonlinearity in Rn
Bisci and Radulescu [5] studied the existence of multiple ground state solutions for a class of parametric fractional Schrödinger equations
Summary
Problem (1.1) is related to the existence of nontrivial meromorphic solutions for the following general Schrödinger equations (see [2, 12, 20] for more details): Lv and Tang [41] employed the mountain pass theorem to obtain the existence of a positive ground state solution for quasilinear Schrödinger equations with a general nonlinear term. Our meromorphic identity subproblem model is defined as follows (see [14]): 1 Min Nl(ς ) = 2
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