zbMATH — the first resource for mathematics

On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem. (English) Zbl 0849.34018
The authors continue their investigation of the solvability of boundary value problems associated with the second order differential equation (*) $$u' + f(u) = p(t,u,u')$$, $$t \in [a,b]$$, where no a priori bound for solutions may be proved. This fact requires a modification of the classical Leray-Schauder continuation technique. This modification was essentially established in the authors’ paper published in [J. Differ. Equations 88, 347-395 (1990; Zbl 0718.34053)].
Reviewer: O.Došlý (Brno)

MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 47J05 Equations involving nonlinear operators (general)
Full Text: