Dehong Ji, Weigao Ge, "Existence of Positive Solutions to a Four-Point Boundary Value Problems," WSEAS Transactions on Mathematics, vol. 11, pp. -, 2012, DOI:
Dehong Ji, Weigao Ge. Existence of Positive Solutions to a Four-Point Boundary Value Problems.
WSEAS Transactions on Mathematics. 2012;11:-.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Existence of Positive Solutions to a Four-Point Boundary Value Problems
Authors: ,
Abstract: By using the fixed point theorem of cone expansion and compression of norm type and monotone iterative technique, we study the following equation <br> $$(ϕp(u^{′}(t)))^{′} + λq(t)f(t, u(t)) = 0, t ∈ (0, 1),$$ <br> and <br> $$(ϕp(u^{′}(t)))^{′} + q(t)f(t, u(t), u^{′}(t)) = 0, t ∈ (0, 1),$$ subject to boundary conditions: <br> $$u^{′}(0) − αu(ξ) = 0, u^{′}(1) + βu(η) = 0,$$ where $$ϕp(s) = |s|^{p−2}· s, p > 1,$$ the existence and iteration of positive solutions are proved. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly in section 3.
Keywords:
Positive solutions, p−Laplacian, Boundary value problem, Monotone iterative technique, Completely continuous, Cone
Pages: - WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 11, 2012DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
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