Radial solutions for a quasilinear elliptic system of Schr\"odinger type

TL;DR

This paper investigates the existence of radially symmetric solutions to a class of quasilinear elliptic Schrödinger systems involving p-Laplacian operators, with conditions on the functions and parameters ensuring solutions on the entire space.

Contribution

It provides new existence results for radially symmetric solutions to a broad class of quasilinear Schrödinger systems with variable coefficients.

Findings

Existence of entire radially symmetric solutions established.

Conditions on functions h_i, a_i, and f_i ensure solutions.

Results extend previous work on scalar equations to systems.

Abstract

In this paper we analyze the existence of entire radially symmetric solutions for Schrodinger system type {\Delta}_{p_{i}}u_{i}+h_{i}(r)|\nabla u_{i}|^{p_{i}-1}=a_{i}(r)f_{i}(u_1,...,u_{d}) for i=1,...,d on R^{N} where p_{i}>1, d \in {1,2,3,...}, h_{i} and a_{i} are nonnegative radial continuous functions and f_{i} are nonnegative increasing continuous functions on [0,\infty).