Periodic solutions of some Liénard equations with singularities

Abstract

Abstract.We consider the forced Liénard equationtogether with the boundary conditionswhere g is continuous on R x (0, +oo) and becomes infinite at u = 0. We consider classical solutions as well as generalized solutions that can go into the singularity u = 0 . The method of approach uses upper and lower solutions and degree theory.

Generalized upper and lower solution method for the forced Duffing equation

“…Our results generalize or extend some famous results obtained by Mawhin(1985), Habets(1990), Nkashama(1989) and Nieto(1990).…”

Second order singular periodic problems in the presence of dry friction

“…Analogous results for the case where dissipation is present were obtained in [8] and more recently in [1].…”

Bubbling solutions for supercritical problems on manifolds

“…If (2.2) holds, the claim follows by Proposition 1 of [10] and if (2.3) holds the claim follows by Theorem 1.1 of [4].…”

“…Moreover, the nonlinear operator ψ satisfies a Lipschitz condition of the form 10) for some positive constant c independent on ǫ.…”