Singular Dirichlet second-order BVPs with impulses

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

A Note on the Paper “ Multipoint BVPs for Second - Order Differential Equations with Impulses ”

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...

Oscillation criteria for second order nonlinear dynamic equations with impulses

We investigate the oscillatory behavior of the second order nonlinear dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = 0, the forced dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) and the forced-perturbed dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) + p(t)x (t). The obtained results are new and not only extend the known results appeared in the literature, but they also improve and unify the kn...

Stability Analysis for Nonlinear Second Order Differential Equations with Impulses∗

In this paper we investigate the impulsive equation { (r(t)x′) + a(t)x + f (t, x, x′) = p(t), t ≥ t0, t 6= tk, x(tk) = ckx(tk − 0), x(tk) = dkx(tk − 0), k = 1, 2, 3, . . . , and establish a couple of criteria to guarantee the equations of this type to possess the stability, including boundedness and asymptotic properties. Some examples are given to illustrate our results and the last one shows ...