MULTIPLICITY AND LOCATION RESULTS FOR SECOND ORDER FUNCTIONAL BOUNDARY VALUE PROBLEMS

Abstract

In this work it is presented some existence, non-existence and location results for the problem composed by the second order fully nonlinear equation with a real parameter s and functional boundary conditions satisfying some adequate monotonicity assumptions. It will be done a discussion on s about the existence and non-existence of solutions for problem (E)-(BC): More precisely, there are s0; s1 2 R such that: for s < s0 or (s > s0) there is no solution of (E)-(BC). for s = s0 problem (E)-(BC) has one solution. The arguments used apply lower and upper solutions technique, a Nagumo condition and a priori estimations.