Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Exact multiplicity results for boundary value problems with nonlinearities generalising cubic

Philip Kormana1*, Yi Lia2 and Tiancheng Ouyanga3

a1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, U.S.A.

a2 Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.

a3 Department of Mathematics, Brigham Young University, Provo, Utah 84602, U.S.A.

Using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type

S0308210500022927_eqnU1

The first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u. The second one deals with a class of nonlinearities with explicit x dependence.

(Received June 15 1994)

(Revised January 18 1995)

Footnotes

* Supported in part by the Taft Faculty Grant at the University of Cincinnati

† Supported in part by the National Science Foundation

‡ Supported in part by a College of Science Research Grant, Brigham Young University