A three point boundary value problem for nonlinear fourth order differential equations

In this paper, the authors consider the nonlinear fourth order ordinary differential equation u (t ) = λg(t)f (u), 0 < t <1, (E) with the boundary conditions u(0) = u (1) = u (0) = u (p)− u (1) = 0. (B) Some results on the existence and nonexistence of positive solutions to problem (E)–(B) are obtained. Results on the existence of infinitely many positive solutions are also presented. Examples are included to demonstrate that the results are sharp.  2003 Elsevier Inc. All rights reserved