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