Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian

Abstract

In this paper we prove the existence and multiplicity of subharmonic solutions for nonlinear equations involving the singular φ-Laplacian. Such equations are in particular motivated by the one-dimensional mean curvature problems and by the acceleration of a relativistic particle of mass one at rest moving on a straight line. Our approach is based on phase-plane analysis and an application of the Poincaré-Birkhoff twist theorem.

Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

“…Notice that in the above corollaries g k would not necessarily satisfy the quasi-linear growth assumption in (A 1 ). Hence, we generalize to higher dimensional systems of related results obtained in [5,9,10,26] for scalar second order differential equations or relativistic equations.…”