Solvability of an elastic beam equation in presence on a sign-type Nagumo control

Abstract

The aim of this work is to establish an existence and localization result for the fourth order two-point boundary value problem

u^(iv) = f (x;u;u';u'';u''') ; 0 < x < 1; u(0) = u'(1) = u''(0) = u'''(1) = 0; related to elastic beam models. It is assumed that f : [0;1]*R4-> R is a continuous function satisfying a sign-type Nagumo growth condition which allows an asymmetric unbounded behavior on the nonlinearity. The arguments make use of the lower and upper solution method and degree theory.