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Existence of Three Positive Solutions for a Nonlocal Singular Dirichlet Boundary Problem
J. Giacomoni, , K. Sreenadh
Published in De Gruyter
Volume: 19
Issue: 2
Pages: 333 - 352
In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem: (Equation Presented), where (-Δ) s denotes the fractional Laplace operator for s ∈ (0, 1), n > 2s, q ∈ (0, 1), λ > 0 and Ω is a smooth bounded domain in ℝ n . Here f : [0, ∞) → [0, ∞) is a continuous nondecreasing map satisfying (Equation Presented). We show that under certain additional assumptions on f, the above problem possesses at least three distinct solutions for a certain range of λ. We use the method of sub-supersolutions and a critical point theorem by Amann [H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), no. 4, 620.709] to prove our results. Moreover, we prove a new existence result for a suitable infinite semipositone nonlocal problem which played a crucial role to obtain our main result and is of independent interest. © 2019 Walter de Gruyter GmbH.
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JournalData powered by TypesetAdvanced Nonlinear Studies
PublisherData powered by TypesetDe Gruyter