Accession Number : AD0701683

Title :   NON-LINEAR EIGENVALUE PROBLEMS FOR SOME FOURTH ORDER EQUATIONS. II. FIXED POINT METHODS.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES

Personal Author(s) : Parter,Seymour V.

Report Date : NOV 1969

Pagination or Media Count : 51

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)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, *NUMERICAL INTEGRATION), PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, INTEGRAL EQUATIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE