Singular \(\phi\)-Laplacian third-order BVPs with derivative dependence. (English) Zbl 1374.34067

Djebali, Smaïl; Saifi, Ouiza

Arch. Math., Brno 52, No. 1, 35-48 (2016).

Summary: This work is devoted to the existence of solutions for a class of singular third-order boundary value problems associated with a \(\phi\)-Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotone with respect to its arguments and may have a space singularity; however no Nagumo-type condition is assumed. An example illustrates the applicability of the existence result.

MSC:

34B16	Singular nonlinear boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40	Boundary value problems on infinite intervals for ordinary differential equations
47H10	Fixed-point theorems

Keywords:

third-order boundary value problem; half-line; \(\phi\)-Laplacian; singular problem; positive solution; derivative dependance; upper and lower solution