Multiple positive solutions for the one-dimensional singular p-Laplacian

Authors:
Haishen Lü;Donal O'Regan;Chengkui Zhong
Affiliations:
Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China;Department of Mathematics, National University of Ireland, Galway, Ireland;Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

We consider the following boundary value problem: (φp(y'))' + q(t)f(y) = 0, p 1, t ∈ [0, 1], with y(0) =y(1) = 0, or y(0) =y'(1) = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. An example is also included to illustrate the importance of the result obtained.