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### Antiperiodic boundary value problems for finite dimensional differential systems.

Boundary Value Problems [electronic only]

### Antiperiodic boundary value problems for second-order impulsive ordinary differential equations.

Boundary Value Problems [electronic only]

### Construction of non-constant lower and upper functions for impulsive periodic problems.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects

Annales Polonici Mathematici

Some sufficient conditions on the existence and multiplicity of solutions for the damped vibration problems with impulsive effects ⎧ u”(t) + g(t)u’(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T ⎨ u(0) = u(T) = 0 ⎩ $\Delta {u}^{\text{'}}\left({t}_{j}\right)={u}^{\text{'}}\left(t{⁺}_{j}-{u}^{\text{'}}\left(t{¯}_{j}\right)={I}_{j}\left(u\left({t}_{j}\right)\right)$, j = 1,...,p, are established, where $t₀=0, g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and ${I}_{j}:ℝ\to ℝ$, j = 1,...,p, are continuous. The solutions are sought by means of the Lax-Milgram theorem and some critical point theorems. Finally, two examples are presented to illustrate the effectiveness of our results....

### Existence and uniqueness of positive solutions for Neumann problems of second order impulsive differential equations.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

Open Mathematics

This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure...

### Existence of nonzero solutions for a class of damped vibration problems with impulsive effects

Applications of Mathematics

In this paper, a class of damped vibration problems with impulsive effects is considered. An existence result is obtained by using the variational method and the critical point theorem due to Brezis and Nirenberg. The obtained result is also valid and new for the corresponding second-order impulsive Hamiltonian system. Finally, an example is presented to illustrate the feasibility and effectiveness of the result.

### Existence of positive solution for second-order impulsive boundary value problems on infinity intervals.

Boundary Value Problems [electronic only]

### Existence of positive solutions for multipoint boundary value problem on the half-line with impulses.

Boundary Value Problems [electronic only]

### Existence of solutions and nonnegative solutions for prescribed variable exponent mean curvature impulsive system initialized boundary value problems.

Journal of Inequalities and Applications [electronic only]

### Existence of solutions for a class of second-order $p$-Laplacian systems with impulsive effects

Applications of Mathematics

The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system $\begin{array}{c}\frac{\mathrm{d}}{\mathrm{d}t}\left(|\stackrel{˙}{u}\left(t\right){|}^{p-2}\stackrel{˙}{u}\left(t\right)\right)=\nabla F\left(t,u\left(t\right)\right),\phantom{\rule{1.0em}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in \left[0,T\right],\\ u\left(0\right)-u\left(T\right)=\stackrel{˙}{u}\left(0\right)-\stackrel{˙}{u}\left(T\right)=0,\\ \Delta {\stackrel{˙}{u}}^{i}\left({t}_{j}\right)={\stackrel{˙}{u}}^{i}\left({t}_{j}^{+}\right)-{\stackrel{˙}{u}}^{i}\left({t}_{j}^{-}\right)={I}_{ij}\left({u}^{i}\left({t}_{j}\right)\right),\phantom{\rule{4pt}{0ex}}i=1,2,\cdots ,N;\phantom{\rule{4pt}{0ex}}j=1,2,\cdots ,m.\end{array}$ By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$-Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.

### Existence of solutions for second-order nonlinear impulsive differential equations with periodic boundary value conditions.

Boundary Value Problems [electronic only]

### Existence of solutions for second-order nonlinear impulsive boundary-value problems.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Existence of solutions of impulsive boundary value problems for singular fractional differential systems

Mathematica Bohemica

A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point...

### Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses.

Advances in Difference Equations [electronic only]

### Existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales.

Advances in Difference Equations [electronic only]

### First order impulsive differential inclusions with periodic conditions.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### Impulsive boundary value problems for $p\left(t\right)$-Laplacian’s via critical point theory

Czechoslovak Mathematical Journal

In this paper we investigate the existence of solutions to impulsive problems with a $p\left(t\right)$-Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...

### Impulsive periodic boundary value problem

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the paper we consider the impulsive periodic boundary value problem with a general linear left hand side. The results are based on the topological degree theorems for the corresponding operator equation $\left(I-F\right)u=0$ on a certain set $\Omega$ that is established using properties of strict lower and upper functions of the boundary value problem.

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