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