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
$$(ϕp(u^{′}(t)))^{′} + λq(t)f(t, u(t)) = 0, t ∈ (0, 1),$$
and
$$(ϕp(u^{′}(t)))^{′} + q(t)f(t, u(t), u^{′}(t)) = 0, t ∈ (0, 1),$$ subject to boundary conditions:
$$u^{′}(0) − αu(ξ) = 0, u^{′}(1) + βu(η) = 0,$$ 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.