On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem. (English) Zbl 0849.34018

Capietto, Anna; Mawhin, Jean; Zanolin, Fabio

Topol. Methods Nonlinear Anal. 6, No. 1, 175-188 (1995).

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)

Keywords:

nonlinear Sturm-Liouville BVP; coincidence degree; boundary value problems; second order differential equation; Leray-Schauder continuation technique