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Positive solutions for one-dimensional singular p-Laplacian boundary value problems

Huijuan Song, Jingxue Yin, Rui Huang (2012)

Annales Polonici Mathematici

We consider the existence of positive solutions of the equation 1 / λ ( t ) ( λ ( t ) φ p ( x ' ( t ) ) ) ' + μ f ( t , x ( t ) , x ' ( t ) ) = 0 , where φ p ( s ) = | s | p - 2 s , p > 1, subject to some singular Sturm-Liouville boundary conditions. Using the Krasnosel’skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.

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