Abstract
The main goal of this paper is to study the general Schrödinger\t\t\t\tequations with a superlinear Neumann boundary value problem in domains with conical\t\t\t\tpoints on the boundary of the bases. First the formulation and the complex form of\t\t\t\tthe problem for the equations are given, and then the existence result of solutions\t\t\t\tfor the above problem is proved by the complex analytic method and the fixed point\t\t\t\tindex theory, where we absorb the advantages of the methods in recent works and give\t\t\t\tsome improvement and development. Finally, we are also interested in the asymptotic\t\t\t\tbehavior of solutions of the mentioned equation. These results generalize some\t\t\t\tprevious results concerning the asymptotic behavior of solutions of non-delay\t\t\t\tsystems of Schrödinger equations or of delay Schrödinger equations.
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