Tenth MSU Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 23 (2016), pp. 77-86.

Multiplicity of solutions of relativistic-type systems with periodic nonlinearities: a survey

Jean Mawhin

Abstract:
We survey recent results on the multiplicity of T-periodic solutions of differential systems of the form
$$ \Big(\frac{u'}{\sqrt{1 - |u'|^2}}\Big)' + \nabla_u F(t,u) = e(t) $$
when $F(t,u)$ is $\omega_i$-periodic with respect to $u_i$ $(i = 1,\ldots,N)$. Several techniques of critical point theory are used.

Published March 21, 2016.
Math Subject Classifications: 34C15, 34C25, 58E05.
Key Words: Pendulum-type equations; multiple solutions; critical point theory; Ljusternik-Schnirelmann category.

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Jean Mawhin
Institut de Recherche en Mathématique et Physique
Université Catholique de Louvain
1348 Louvain-la-Neuve, Belgium
email: jean.mawhin@uclouvain.be

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