Positive solutions for singular \(\phi\)-Laplacian BVPs on the positive half-line. (English) Zbl 1201.34040

Djebali, Smaïl; Saifi, Ouiza

Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 56, 24 p. (2009).

The authors are concerned with the existence of multiple positive solutions for a \(\phi\)-Laplace boundary value problem on the half-line. The nonlinearity may exhibit a singularity at the origin with respect to the state variable. The results are proved by using the fixed point index theory on cones and the upper and lower solution method.

Reviewer: Pierpaolo Omari (Trieste)

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34B40	Boundary value problems on infinite intervals for ordinary differential equations
34B16	Singular nonlinear boundary value problems for ordinary differential equations
47H20	Semigroups of nonlinear operators

Keywords:

positive solution; \(\phi\)-Laplace operator; half-line; singular problem; fixed point index on cones; lower and upper solution