ON A 3RD-ORDER NONLINEAR BOUNDARY-VALUE PROBLEM AT RESONANCE

In this paper we discuss the existence of solutions to third order boundary value problems of the form x''' + x' + g(x, x') = p(t), x'(0) = x'(pi) = x(eta) = 0, where eta lies in [0, pi]. We assume that g is continuous and one-sided bounded (e.g., g greater than or equal to 0) and p is continuous. Solutions are shown to exist if p satisfies a Landesman-Lazer type condition involving g. Several examples are given to illustrate how these conditions depend upon the parameter eta. (C) 1995 Academic Press, Inc.