Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional \(p\)-Laplacian. (English) Zbl 1224.34046

Naito, Y.

Math. Bohem. 136, No. 2, 175-184 (2011).

Summary: We consider a boundary value problem involving the one-dimensional \(p\)-Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34B08	Parameter dependent boundary value problems for ordinary differential equations

Keywords:

boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation