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Third order BVPs with $$\phi$$-Laplacian operators on $$[0,+\infty)$$. (English) Zbl 1283.34019
Summary: This work deals with the existence of multiple positive solutions for a third-order boundary value problem with a $$\phi$$-Laplacian operator on the halfline. The existence results are obtained both for the regular and the singular cases using the fixed point index theory on a suitable cone of a Banach space. The singularity is treated by an approximation technique and sequential arguments. Examples of applications are included to illustrate the existence results.
##### MSC:
 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 34B16 Singular nonlinear boundary value problems for ordinary differential equations
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##### References:
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