# Exponential Expansiveness and Variational Integral Equations

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This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a...

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In a rectangular domain, we consider a two-dimensional integral equation of Volterra type with fixed singular kernels. For various values of the parameters occurring in this equation, we prove its unique solvability and establish the asymptotic behavior of the obtained solution.

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Classical integral equation techniques used to investigate the solvability of the interior third boundary-value problem in three-dimensional elasticity fail in the two-dimensional case on account of the divergence of the corresponding potential at infinity. In this paper we show how to overcome...

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Discrete multidimensional singular integral equations with Calderon-Zygmund kernels are considered in a discrete half-space. The solvability of such equations is studied using the properties of discrete Fourier transform and corresponding properties of Calderon-Zygmund operators.

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The work defines the conditions of solvability of one integral convolutional equation with degreely difference kernels in a singular case. This type of integral equations was not studied earlier, and it turned out that all methods used for the investigation of such equations with the help of...

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A structural equation modelling approach for estimating a linear growth curve model is presented. This method can be used for a wide variety of models based on the General Linear Mixed Model. This model is a simple example of a multilevel or random coefficients model. The logic of the method is...

- WEIGHTED $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{L}_{{P}}$ SOLVABILITY ... TANG, LIN // Journal of the Australian Mathematical Society;Jun2014, Vol. 96 Issue 3, p396
We consider the weighted $L_p$ solvability for divergence and nondivergence form parabolic equations with partially bounded mean oscillation (BMO) coefficients and certain positive potentials. As an application, global regularity in Morrey spaces for divergence form parabolic operators with...

- To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point. Rajabov, Nusrat // Applied Mathematics;Sep2013, Vol. 4 Issue 9, p1301
In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three...

- Numerical treatment of boundary value problems by solving a system of second kind Fredholm integral equations. Frammartino, Carmelina // Calcolo;Jun2013, Vol. 50 Issue 2, p123
A NystrÃ¶m method is proposed for solving systems of Fredholm integral equations equivalent to special boundary value problems of order $$2s$$. The stability and the convergence of the proposed procedure is proved. The GMRes method is applied to solve the involved systems of linear equations....