Work

Positive solutions of Schrödinger equations with potentials G-symmetric and vanishing at infinity

Year: 2026

Type: article

Abstract: We study the existence of a positive solution for a class of nonlinear Schrödinger equations $$\begin{aligned} -\Delta u+V(x)u=f(u), \qquad u \in \mathcal {D}^{1,2}(\mathbb {R}^N), \ N\ge 3. \end{aligned}$$ - Δ u + V ( x ) u = f ( u ) , u ∈ D 1 , 2 ( R N ) , N ≥ 3 . Here the potential V is symmetric under a group action $$G \subset O(N)$$ G ⊂ O ( N ) and decay to zero at infinity, and the nonlinearity f , under very mild hypotheses, is asymptotically linear or superlinear and subcritical at infinity, not satisfying any monotonicity condition.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-026-01196-1

Authors: G. S. Pina, R. D. Carlos, R. Ruviaro

Institutions: Universidade Federal do Recôncavo da Bahia, Universidade de Brasília

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Universidade de Brasília