New type of solutions for the nonlinear Schrodinger equation in RN

We construct a new family of entire solutions for the nonlinear Schrodinger equation {-Delta u + V (y) u = u(p), u > 0, in R-N, u is an element of H-1 (R-N), where p is an element of (1, N+2/N-2)) and N >= 3, and V(y) = V(vertical bar y vertical bar) is a positive bounded radial potential satisfying V(vertical bar y vertical bar) = V0 + a/vertical bar y vertical bar(m) + O (1/' y '(m+sigma), as vertical bar y vertical bar -> infinity, for some fixed constants V-0, a, sigma > 0, and m > max{4/p-1, 2}. (c) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This study constructs a new family of entire solutions for the nonlinear Schrodinger equation, which has wide applications in the entire space. The research findings indicate that, under certain conditions, the equation has solutions that satisfy specific constraints and conditions.