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Positive periodic solutions of singular third-order functional differential equations with \(p\)-Laplacian-like operators. (English) Zbl 1452.34076

Summary: The aim of this paper is to consider singular third-order functional differential equations with \(p\)-Laplacian-like operator of the form \[\left(\varphi_p\left(x''\left(t\right)\right) \right)' + f\left(t,x\left(t - \tau\right)\right) = e\left(t\right).\] Unlike in previous works, \(f\) has a strong singularity at \(x = 0\) and satisfies a small force condition at \(x = \infty \). Based on a continuation theorem due to Mawhin, new results on the existence of positive periodic solutions are obtained, which makes it possible to refine and extend some related results in the literature. A typical example demonstrating the effectiveness and flexibility of the main results is given.

MSC:

34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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