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Some integral type boundary value problems (BVPs) for second order differential equations (ODEs) with one-dimensional p-Laplacian on the whole line are discussed. Sufficient conditions to guarantee the existence of solutions are established. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x'(t))]' involved with the nonnegative function ρ that may satisfy $\rho(0)=0$, and the differential equations are defined on the whole line.

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term [Φ(ρ(t)x'(t))]' involved with the nonnegative singular function ρ and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Boundary value problems of second-order singular differential equations with nonlinear operator Φ on whole lines are discussed. By applying the nonlinear alternative of Leray-Schauder-type fixed point theorem, some existence results of solutions for integral boundary value problems of differential equations on whole lines are established. The emphasis is put on the nonlinear operator [Φ(ρ(t)x′(t))]′ involved with the nonnegative function ρ that may satisfy ρ(0) = 0, the strictly increasing sup-multiplicative-like function Φ and the differential equations are defined on the whole line. Three examples and a remark are presented to illustrate the main theorems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation    [Φ(ρ(t)x 0 (t))]0 + f(t, x(t), x0 (t)) = 0, t ∈ R, limt→−∞ x(t) = R +∞ −∞ g(s, x(s), x0 (s)) ds, limt→+∞ ρ(t)x 0 (t) = R +∞ −∞ h(s, x(s), x0 (s)) ds. Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x 0 (t))]0 involved with the nonnegative function ρ satisfying R +∞ −∞ 1/ρ(s) ds = +∞.

This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the one-dimensional p-Laplacian term involving a nonnegative function ρ that may be singular at t = 0 and such that . A Banach space and a nonlinear completely continuous operator are defined in this paper. By using the Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established. An example is presented to illustrate the main theorem.

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian {[p(t)Φ(x'(t))]'+f(t,x(t),(t))=0, tϵ(0,1), ø1(x(0))=∫01 g(s)ø1(s(s))ds, ø2(x'(1))=∫01h(s)ø2(x'(s)) ds. Sufficient conditions to guarantee the existence of at least three positive solutions of this BVP are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [p(t)Φ(x'(t))]' involved with the function r, which makes the solutions un-concave. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive solutions for some boundary value problems of the singular differential equations on the whole line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of nonneg-ative solutions for the problems, but also establish iterative schemes for approximating the solutions. [ABSTRACT FROM AUTHOR]