NON-LINEAR EIGENVALUE PROBLEMS FOR SOME FOURTH ORDER EQUATIONS. I. MAXIMAL SOLUTIONS.
WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES
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A constructive, nonlinear iterative method is developed for the construction of a positive solution ut, thetat of a nonlinear fourth order ordinary differential equation of the form U double prime lambda thetaH sub 1t,u, theta, theta double prime lambda uH sub thetat,u, theta. A solution ut, thetat is positive if ut or 0 or thetat. 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
- Theoretical Mathematics