A Mountain Pass Theorem for a Suitable Class of Functions (original) (raw)

A three critical points theorem and its applications to the ordinary Dirichlet problem

Topological Methods in Nonlinear Analysis, 2003

The aim of this paper is twofold. On one hand we establish a three critical points theorem for functionals depending on a real parameter λ ∈ Λ, which is different from the one proved by B. Ricceri in and gives an estimate of where Λ can be located. On the other hand, as an application of the previous result, we prove an existence theorem of three classical solutions for a two-point boundary value problem which is independent from the one by J. Henderson and H. B. Thompson ([10]). Specifically, an example is given where the key assumption of [10] fails. Nevertheless, the existence of three solutions can still be deduced using our theorem.

Critical point theorems with relaxed boundary condition and applications

Bulletin of the Australian Mathematical Society, 1993

This paper is a sequel to a recent paper by the author in this journal. We prove some variants of the min-max type critical point theorems with relaxed boundary condition and then apply the abstract results to a semilinear elliptic boundary value problem.

On a variational problem with lack of com-pactness: the topological e0ect of the critical points at

1995

R6sum6. Nous 6tudions les probl~mes sous-critiques (Pc) 9 -Au = u p-e, u > 0 sur f2 ; u = 0 sur 0f2 -of a f2 est un domaine born6 et r6gulier de ~N N > 3,p+ 1 = N-2-~-----7 est l'exposant critique de Sobolev, et e > 0 tend vers z6ro, afin de calculer la diff6rence de toplogie induite par les points critiques h l'infini entre les ensembles de niveau de la fonctionnelle correspondant au cas limite (P0).

Critical point theory for nondifferentiable functionals and applications

Journal of Mathematical Analysis and Applications, 1990

We consider minimization results for locally Lipschitzian functionals on a Banach space by introducing a compactness condition of the Palais-Smale type which is suggested by the Variational Principle of Ekeland. Applications are given to some semilinear elliptic problems with discontinuous nonlinearities.