Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale. (English) Zbl 1005.34010

Davis, John M.; Henderson, Johnny; Prasad, K. Rajendra; Yin, William

Abstr. Appl. Anal. 5, No. 2, 91-99 (2000).

Summary: The authors consider the nonlinear second-order conjugate eigenvalue problem on a time scale: \(y^{\Delta\Delta}(t) + \lambda a(t) f(y(\sigma(t))) = 0, t \in [0,1], y(0) = 0 = y(\sigma(1))\). Values of the parameter \(\lambda\) (eigenvalues) are determined for which this problem has a positive solution. The methods used here extend recent results by allowing for a broader class of functions for \(a(t)\).

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34L30	Nonlinear ordinary differential operators

Keywords:

nonlinear second-order conjugate eigenvalue problem; positive solution