Eigenvalues and the One-Dimensional p-Laplacian |
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Authors: | Ravi P AgarwalHaishen Lü Donal O'Regan |
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Institution: | a Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida, 32901-6975b Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of Chinac Department of Mathematics, National University of Ireland, Galway, Ireland |
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Abstract: | We consider the boundary value problem (?p(u′))′ + λF(t, u) = 0, with p > 1, t ∈ (0, 1), u(0) = u(1) = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed. |
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Keywords: | positive solutions boundary value problems |
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