Relativistic equations with singular potentials

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URI: https://hdl.handle.net/10481/83810
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Autor
Arcoya Álvarez, David; Sportelli, Caterina
Editorial
Springer Nature
Materia
Lorentz force equation
 
Relativistic pendulum equation
 
Mountain pass theorem
 
Global continuation theorem
 
Fecha
2023-04-17
Referencia bibliográfica
Arcoya, D., Sportelli, C. Relativistic equations with singular potentials. Z. Angew. Math. Phys. 74, 91 (2023). [https://doi.org/10.1007/s00033-023-01977-z]
Patrocinador
Universidad de Granada/CBUA; Spanish Government PGC2018-096422-B-I00, PID2021-122122NB-I00; Junta de Andalucia FQM-116; Ministry of Education, Universities and Research (MIUR) 2017JPCAPN_005
Resumen
The first part of this paper concern with the study of the Lorentz force equation [GRAPHICS] in the relevant physical configuration where the electric field (E) over right arrow has a singularity in zero. By using Szulkin's critical point theory, we prove the existence of T-periodic solutions provided that T and the electric and magnetic fields interact properly. In the last part, we employ both a variational and a topological argument to prove that the scalar relativistic pendulum-type equation [GRAPHICS] admits at least a periodic solution when h is an element of L-1(0, T) and G is singular at zero.
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Atribución 4.0 Internacional
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