Wendy F. Almeida, Giovany M. Figueiredo
Abstract:
This work addresses the existence of at least one radial solution to the
nonlinear magnetic Schrodinger equation
$$
\Big(\frac{\epsilon}{i} \nabla - A(x) \Big)^2 u + V(x) u = f(|u|^2) u \quad
\text{in } \mathbb{R}^N,
$$
where both the magnetic potential \(A\) and the electric potential \(V\) are continuous,
radial functions. Our main tool is the penalization method developed by del Pino
and Felmer [17], which we adapt to the complex-valued setting under magnetic
effects. By using the small parameter \(\epsilon\) and radial symmetry, we
handle nonlinearities with arbitrary growth.
Submitted September 27, 2025. Published November 24, 2025.
Math Subject Classifications: 35B33, 35J20, 35Q55.
Key Words: Magnetic Schrodinger equations; arbitrary growth at infinity.
DOI: 10.58997/ejde.2025.110
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Wendy F. Almeida
Universidade de Brasília Departamento de Matemática Campus Darcy Ribeiro, 01 CEP 70910-900, Brasília, DF, Brazil email: wendy_fda@hotmail.com |
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Giovany M. Figueiredo Universidade de Brasília Departamento de Matemática Campus Darcy Ribeiro, 01 CEP 70910-900, Brasília, DF, Brazil email: giovany@unb.br |
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