Multiple positive solutions for a semipositone fourth-order boundary value problem

By Ruyun Ma. 2003

54 citations recorded by the source corpus.

We consider the nonlinear fourth order boundary value problem u ð4Þ ðx Þ¼ l f ðx; uðxÞ; u 0 ðxÞÞ uð0 Þ¼ u 0 ð0 Þ¼ u 00 ð1 Þ¼ u 000 ð1 Þ¼ 0 where f : ½0; 1 ��½ 0; y Þ�½ 0; y Þ!ð � y; yÞ is continuous with f ðx; u; pÞbM for some positive constant M. We show the existence and multiplicity of positive solutions by using a fixed point theorem in cones.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ed71ee4f6b2a0b4291992fbfa297fa75d218f73c