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A Remark on Some Three‐Point Boundary Value Problems for the One‐Dimensional p ‐Laplacian
Author(s) -
Weigao H.,
Xiaoming G.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200210)82:10<728::aid-zamm728>3.0.co;2-r
Subject(s) - mathematics , value (mathematics) , point (geometry) , laplace operator , mathematical analysis , boundary value problem , boundary (topology) , geometry , statistics
We establish existence criteria for multiple (at least three) positive solutions to the three‐point boundary value problem (g(u′))′ + a(t) f(u) = 0, u(0) = 0 u(η) = u(1), where g(v) ≔ |v| p–2 v, p > 1, and η ∈ (0, 1) is prescribed. The results improve and extend earlier results due to Wang Junyu and Zheng Dawei [1] by an application of the Leggett‐Williams fixed point theorem in a cone.