Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 336, Issue -, Pages 479-504Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.07.027
Keywords
Nonlinear Schrodinger equation; Infinitely many solutions; New solutions; Finite Lyapunov-Schmidt reduction
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Funding
- China Scholarship Council
- NSFC [11771167]
- EPSRC [EP/T008458/1]
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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.
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.
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