A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals J(lambda), lambda is an element of I subset of R. Under suitable assumptions, we locate an open subinterval of values lambda in I for which J(lambda) possesses at least three critical points. Applications to quasilinear boundary value problems are also given. (c) 2006 Elsevier Inc. All rights reserved.