A New Solution Operator of One‐Dimensional p‐Laplacian with a Sign‐Changing Weight and Its Application

Inbo Sim and Yong Hoon Lee

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We establish a new solution operator for the following problem −φp(u′)′ = g, t ∈ (0,1), u(0) = 0 = u(1), where φp(x) = |x|p−2x, p > 1. g may be singular at the boundary or change signs or may not be in L1(0,1) so that this solution operator can cover larger class of g than previously known ones. As an application, by checking complete continuity of the solution operator, we show the existence of nontrivial solutions for p‐Laplacian φp(u′)′ + λh(t)f(u(t)) = 0, t ∈ (0,1), u(0) = 0 = u(1), where λ > 0 a parameter and f ∈ C(ℝ, ℝ) and f(0) > 0 and h may change signs or may be beyond of L1(0,1).

Date: 2012
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https://doi.org/10.1155/2012/243740

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:243740

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