[PDF] Top 20 A second order impulsive Cauchy problem

... abstract second-order impul- sive Cauchy problem modeled in the form ¨ u(t) = Au(t)+ f (t, u(t), u(t)), t ˙ ∈ (−T 0 , T 1 ), t ≠ t i ; u(0) = x 0 , u(0) ˙ = y 0 ; u(t i ) = I i 1 (u(t i )), ... See full document

... and Hölder’s inequality, the authors showed the existence of countably many positive so- lutions. The other related results can be found in [–]. However, there are almost no papers considering ... See full document

... with second-order differential equations emerge in a variety of areas of applied mathematics and ...value problem, under certain growth conditions on the nonlinearity f , and several sufficient ... See full document

... some second-order boundary value problem with impulsive effects on an unbounded ...for second-order differential equation on the ... See full document

... indefinite problem has attracted the attention of Ma and Han [58], López-Gómez and Tellini [59], Boscaggin and Zanolin [60], Feltrin and Zanolin [61], Boscaggin et ... See full document

... nonlinear second-order double impulsive differential equations integral boundary value problem with p-Laplacian on an infinite interval with the infinite number of impulsive ... See full document

... years, impulsive differential equations have become a very active area of research and we refer the reader to the monographs [8] and the articles [6, 9, 10, 14, 15], where properties of their solutions are studied ... See full document

... x · y is the scalar product, and ∇F(x − tξ) is the gradient with respect to the coordinates x − tξ . Next, we apply the mean-value theorem to the first and the third integrals in the right-hand side of the last formula. ... See full document

... first-or second-order neutral differential equations were established in ...the second order impulsive differential equations is not yet perfect compared to the second order ... See full document

... Based on the understanding of the relativistic dynamics fundamental equation, mathe- maticians put forward relativistic operators which have a close relationship with physics. In recent years, the research of ... See full document

... It is well accepted that fixed point theorems in cones have been instrumental in showing the existence, multiplicity of positive solutions of various boundary value problems for differential equations. See, for instance, ... See full document

... Throughout this problem we assume that there exists an evolution operator S(t, s) associated to the operator A(t). To abbreviate the teϑ, we introduce the operator C(t, s) = − ∂S(t,s) ∂s . In addition, we set N ... See full document

... The rest of this paper is organized as follows. In Section  we present several defini- tions and main tools. In Section , under suitable hypotheses, we prove that problem (.) possesses at least one non-zero ... See full document

... of second-order nonlinear impulsive differen- tial equations is introduced and the existence result is also ...Lagrange problem (P) is ... See full document

... in impulsive differential equations, see the monographs of Lakshmikantham et ...for second-order boundary value problem of impulsive differential equations on time scales by using ... See full document

... the impulsive Dirichlet ...linear problem are basic but crucial to revealing that a problem can be solved by finding the critical points of a ... See full document

... α =   , f (t) =   ( T  – t), g(t) = | h(t) | . Then all the conditions of Theorem . are satisfied. According to Theorem ., the above problem has at least one weak solution. However, F does not satisfy the ... See full document

... for problem P with Dirichlet boundary condition and the existence and nonexistence part of the result for problem P with two-point boundary ...following second-order impulsive ... See full document

... Second-order differential equations with the p-Laplacian operator arise in modeling some physical and natural phenomena and can occur, for example, in non-Newtonian mechan- ics, nonlinear elasticity, ... See full document

... our problem can be reduced to the study of an abstract differential equation associated to some nonlocal boundary conditions involving a linear un- bounded ...our problem can be transformed by a natural ... See full document