[PDF] Top 20 Global existence and asymptotic behavior of solution of second order nonlinear impulsive differential equations

... Proof. We omit the proof as it is virtually the same as that of Theorem 2.1. Theorem 2.8. Suppose that the assumptions of Theorem 2.6 are satisfied for any γ ∈ R. If (2.25) hold for all c > 0, then for any γ ∈ R, ... See full document

... For global existence and asymptotic behavior of solutions to more higher order wave equations, we refer to [–] and references ... See full document

... a global existence and a regularity result of the problem ...the solution decays exponentially if g behaves like a linear function, whereas the decay is of a polynomial order ... See full document

... local solution and the existence of a global ...the global existence of W k,p solutions to wave equations with a dispersive ... See full document

... mild solution of second-order nonlinear impulsive differen- tial equations is introduced and the existence result is also ...the existence of optimal controls for a ... See full document

... of impulsive differential equations is an important branch of differential ...of impulsive differential equations emerging as an important area of research, since such ... See full document

... and nonlinear ODEs of second order can arise during many applications in various scientific areas such as physics, biology, chemistry, biophysics, me- chanics, medicine, aerodynamics, economy, atomic ... See full document

... the existence and nonexistence of global solutions for nonlinear wave equations with nonlinear damping and source terms [4, 5, 10, 13, 18] in the past twenty ...the existence and ... See full document

... the asymptotic properties of the solutions of second order differential equations [1] [2] difference equ- ations of the type (E) and/or related equations have been investigated ... See full document

... study impulsive differential equa- ...the existence of solutions for impulsive differential equation boundary value prob- lems ...Neumann nonlinear differen- tial problem in [] (see also [, ... See full document

... We note that we could consider impulsive BVPs with an arbitrary finite number of impulses. However, for clarity and brevity, we restrict our attention to BVPs with one im- pulse. In addition, the di ff erence ... See full document

... Impulsive differential equations, which provide a natural description of observed evo- lution processes, are regarded as important mathematical tools for the better under- standing of several real ... See full document

... In recent years, some classical tools such as some fixed point theorems in cones, topo- logical degree theory and the upper and lower solutions method combined with the mono- tone iterative technique [–] have been ... See full document

... the existence the lacally attractive solution and its extremal solution of second order nonlinear differential ... See full document

... Proof From Lemma ., we have obtained that Eq. (.) has at most one T -periodic so- lution. Thus, to prove Theorem ., it suffices to show that Eq. (.) has at least one T -periodic solution. To do this, we will ... See full document

... generalized nonlinear Gronwall-Bellman-Type integral inequalities with two variables, which include a non-constant term outside the ...partial differential equations with the initial and boundary ... See full document

... the existence of nonoscillatory solutions of second order nonlinear neutral differential ...and nonlinear equa- ...the existence of nonoscillatory ... See full document

... the existence of homoclinic solutions for im- pulsive differential equations by using perturbation ...the existence of homoclinic solutions for Hamiltonian systems via variational ...of ... See full document

... every solution of (1.1) is either oscillatory or tends to zero. Proof. Assume the contrary. Without loss of generality, we may suppose that {x(n)} is an eventually positive solution of (1.1) such that lim ... See full document

... It is not difficult to prove that H ∗ (t, s) and G ∗ (t, s) have similar properties to those of H(t, s) and G(t, s). However, we cannot guarantee that H ∗ (t, s) >  for any t, s ∈ J. This implies that we cannot apply ... See full document