ArticleOriginal scientific text
Title
Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions
Authors 1, 1
Affiliations
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A.
Abstract
We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
Keywords
nonlinear boundary value problems, multiplicity of positive solutions, upper and lower solutions, degree theory
Bibliography
- H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21 (1971), 125-146.
- H. Amann, On the number of solutions of asymptotically superlinear two point boundary value problems, Arch. Rational Mech. Anal. 55 (1974), 207-213.
- D. S. Cohen, Generalized radiation cooling of a convex solid, J. Math. Anal. Appl. 35 (1971), 503-511.
- H. Dang, K. Schmidt and R. Shivaji, On the number of solutions of boundary value problems involving the p-Laplacian, Electron. J. Differential Equations 1 (1996), 1-9.
- D. R. Dunninger and H. Wang, Multiplicity of positive solutions for an elliptic system, preprint.
- D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, FL, 1988.
- K. S. Ha and Y. Lee, Existence of multiple positive solutions of singular boundary value problems, Nonlinear Anal. 28 (1997), 1429-1438.
- S. S. Lin, Positive radial solutions and nonradial bifurcation for semilinear elliptic equations in annular domains, J. Differential Equations 86 (1990), 367-391.