Existence of solutions for nonlinear BVPs of second-order differential equations on measure chains

Existence of Three Monotone Solutions of Nonhomogeneous Multipoint BVPs for Second-Order Differential Equations

Recommended by Jean Mawhin This paper is concerned with nonhomogeneous multipoint boundary value problems of second-order differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three solutions may be not positive of these BVPs are established.

EXISTENCE AND NON-EXISTENCE OF POSITIVE SOLUTIONS OF FOUR-POINT BVPs FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS ON WHOLE LINE

This paper is concerned with four-point boundary value problems of second order singular differential equations on whole lines. The Green’s function G(t, s) for the problem −(ρ(t)x′(t))′ = 0, lim t→−∞ ρ(t)x′(t)− kx(ξ) = lim t→+∞ ρ(t)x′(t) + lx(η) = 0 is obtained. We proved that G(t, s) ≥ 0 under some assumptions which actually generalizes a corresponding result in [Appl. Math. Comput. 217(2)(20...

Existence of Solutions to Second-Order BVPs on Time Scales

2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

On the Existence of Positive Solutions of a Class of Second Order Nonlinear Differential Equations

We present some results on the existence of bounded positive solutions to a class of nonlinear second order ordinary diferential equations by using the Schauder-Tikhonov fixed point theorem. An application to the existence of bounded positive solutions to certain quasilinear elliptic equations in two-dimensional exterior domains is also given.