Positive Solutions of Three-point Boundary-value Problems for P-laplacian Singular Differential Equations
نویسندگان
چکیده
In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem −[φp(u)] = q(t)f(t, u(t)), 0 < t < 1 subject to u(0)− g(u′(0)) = 0, u(1)− βu(η) = 0 or to u(0)− αu(η) = 0, u(1) + g(u′(1)) = 0, where φp is the p-Laplacian operator, 0 < η < 1; 0 < α, β < 1 are fixed points and g is a monotone continuous function defined on the real line R with g(0) = 0 and ug(u) ≥ 0. Our approach is a combination of Nonlinear Alternative of Leray-Schauder with the properties of the associated vector field at the (u, u′) plane. More precisely, we show that the solutions of the above boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at u = 0.
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