Nontrivial solutions of second-order singular Dirichlet systems

Nontrivial solutions of second-order singular Dirichlet systems

where q ∈ C((, ),R), e = (e, . . . , eN )T ∈ C((, ),RN ), N ≥ , and the nonlinear term f (t,u) ∈ C((, )×RN \ {},RN ). We are mainly motivated by the recent excellent works [–], in which singular periodic systems were extensively studied. Let R+ denote the set of vectors of RN with positive components. For a fixed vector v ∈R+ , we say that system (.) presents a singularity at the o...

Nontrivial Solutions of Singular Second Order There-point Boundary Value Problem at Resonance

The singular second order three-point boundary value problem at resonance { x′′(t) = f(t, x(t)), 0 < t < 1, x′(0) = 0, x(η) = x(1), are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where η ∈ (0, 1) is a constant, f is allowed to be singular at both t = 0 and t = 1. The existence results of nontrivial solutions are given by mea...

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray–Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder’s fixed point theorem an...

Twin Positive Periodic Solutions of Second Order Singular Differential Systems

In this paper, we study positive periodic solutions to singular second order differential systems. It is proved that such a problem has at least two positive periodic solutions. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnosel’skĭı fixed point theorem on compression and expansion of cones.

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations