Accession Number : AD0698312

Title :   NON-LINEAR EIGENVALUE PROBLEMS FOR SOME FOURTH ORDER EQUATIONS. I. MAXIMAL SOLUTIONS.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES

Personal Author(s) : Parter,Seymour V.

Report Date : OCT 1969

Pagination or Media Count : 40

Abstract : A constructive, nonlinear iterative method is developed for the construction of a 'positive' solution (u(t), theta(t)) of a nonlinear fourth order ordinary differential equation of the form U double prime = lambda theta(H sub 1)(t,u, theta), theta double prime = lambda u(H sub theta)(t,u, theta). A solution (u(t), theta(t)) is 'positive' if u(t) = or < 0 = or < theta(t). Under appropriate hypothesis, these solutions are 'maximal' in the sense that; if (omega, phi) is any other solution, then u = or < omega, phi = or < theta. Thus, bounds on (u, theta) are a priori bounds on all solutions. Uniqueness is discussed. In special cases these positive solutions may be patched together to give other solutions. (Author)

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

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE