Relativistic type systems with parametric odd nonlinearities. (English) Zbl 1525.34046
The authors consider the equation driven by a nonlinear relativistic operator with odd perturbations and with periodic, Neumann and Dirichlet boundary conditions for which they prove the existence of multiple distinct pairs of nontrivial solutions. Numerous illustrative examples concerning special type of nonlinear terms are provided. The approach is based on critical point theory for convex, lower semicontinuous perturbations of \(C^1\)-functionals developed by A. Szulkin [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 3, 77–109 (1986; Zbl 0612.58011)].
Reviewer: Marek Galewski (Łódź)
MSC:
| 34B08 | Parameter dependent boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47J30 | Variational methods involving nonlinear operators |
Keywords:
relativistic operator; odd perturbation; Fisher-Kolmogorov nonlinearity; Szulkin-type functionalCitations:
Zbl 0612.58011References:
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