NON-LINEAR EIGENVALUE PROBLEMS FOR SOME FOURTH ORDER EQUATIONS. II. FIXED POINT METHODS.
Abstract
Fixed-point theorems are applied to obtain solutions (u sub k(t), theta sub k(t)) of nonlinear fourth order ordinary differential equations of the form u double prime = lambda theta (H sub 1)(t, u, theta), theta double prime = lambda u (H sub 2)(t, u, theta). The solution (u sub k(t), theta sub k(t)) is distinguished by the fact that each function (u sub k(t) or theta sub k(t) has exactly k interior nodal zeros. The basic conditions implying these existence theorems is lambda sub k < lambda < u sub k where lambda sub k and u sub k are the eigenvalues of the linearized problems, linearized about zero and infinity respectively. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1969
- Accession Number
- AD0701683
Entities
People
- Seymour V. Parter
Organizations
- University of Wisconsin–Madison