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M.i. Ramazanov - One of the best experts on this subject based on the ideXlab platform.
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Spectrum of Volterra integral operator of the second kind
2016Co-Authors: Meiramkul M. Amangaliyeva, Muvasharkhan T. Jenaliyev, Madi Ergaliev, M.i. RamazanovAbstract:The article addresses the singular Volterra integral Equation of the second kind, which has the ’incompressible’ kernel. It is shown that the corresponding homogeneous Equation on |λ| ≥ exp{|arg λ|}, arg λ ∈ [−π,π] has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing |λ|. We use the Carleman-Vekua regularization method. We introduce the characteristic integral Equation. We prove that the initial integral Equation has eigen-functions, the multiplicity of which depends on the value of the spectral parameter λ. We prove the solvability theorem of the Nonhomogeneous Equation in a case when the right-hand side of the Equation belongs to a certain class.
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On the spectrum of Volterra integral Equation with the “incompressible” kernel
2014Co-Authors: Meiramkul M. Amangaliyeva, Muvasharkhan T. Jenaliyev, Minzilya T. Kosmakova, M.i. RamazanovAbstract:The article addresses the singular Volterra integral Equation of the second kind which has the “incompressible” kernel. It is shown that the corresponding homogeneous Equation for |λ| > 1 has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing |λ|. The Equation is reduced to Abel Equation by using the regularization method. The eigenfunctions of the Equation are found in an explicit form. We prove the solvability theorem of the Nonhomogeneous Equation in a case when the right-hand side of the Equation belongs to a certain class.
A. Shirikyan - One of the best experts on this subject based on the ideXlab platform.
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Bounded and Almost Periodic Solutions of Linear High‐Order Hyperbolic Equations
Mathematische Nachrichten, 1998Co-Authors: A. Shirikyan, L R VolevichAbstract:The present paper is devoted to investigating high-order strictly hyperbolic operators with nearly constant coefficients. The invertibility of these operators in spaces of functions uniformly bounded or almost periodic in time is established, provided the symbol of the operator in question has no roots in an open strip containing the real line. Under the additional condition that the strip coincides with a half-plane, exponentially decaying solutions of the Nonhomogeneous Equation with right-hand side of exponential decay are constructed. In the case of Equations with constant coef- ficients the necessity of the derived conditions is proved. The results of this paper were announced without proofs in (SV).
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Linear high-order hyperbolic Equations. Bounded and almost periodic in time solutions
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997Co-Authors: A. ShirikyanAbstract:We consider the problem of invertibility of strictly hyperbolic operators with variable coefficients in spaces of functions bounded or almost periodic in time. We present sufficient conditions for the Nonhomogeneous Equation to he solvable in spaces of exponentially decreasing, bounded or almost periodic functions, and for the homogeneous Equation to possess the exponential dichotomy property.
Sami Aouaoui - One of the best experts on this subject based on the ideXlab platform.
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Adams’ type inequality and application to a quasilinear Nonhomogeneous Equation with singular and vanishing radial potentials in $$ \mathbb {R}^4 $$
Annali di Matematica Pura ed Applicata (1923 -), 2019Co-Authors: Sami Aouaoui, Francisco S. B. AlbuquerqueAbstract:In this paper, we establish some Adams’ type inequality for weighted second-order Sobolev spaces in four dimensions. The weights are radial and can have a singular or decaying behavior. This inequality is used to study some Nonhomogeneous quasilinear elliptic Equation.
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Existence result for some elliptic quasilinear Equation involving the N -Laplacian in $$ \mathbb {R}^N $$ R N with a large class of nonlinearities
Ricerche di Matematica, 2018Co-Authors: Sami AouaouiAbstract:In this paper, we establish some existence and uniqueness results for a Nonhomogeneous Equation whose nonlinear term can have a critical exponential growth at infinity. The case of a discontinuous nonlinearities is also analyzed. Our main tools are the degree theory for $$ (S_+) $$ operators and a fixed point theorem for Banach semilattice.
V. V. Kornev - One of the best experts on this subject based on the ideXlab platform.
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Classical and Generalized Solutions of a Mixed Problem for a Nonhomogeneous Wave Equation
Computational Mathematics and Mathematical Physics, 2019Co-Authors: A. P. Khromov, V. V. KornevAbstract:A.N. Krylov’s ideas concerning convergence acceleration for Fourier series are used to obtain explicit expressions for the classical solution of a mixed problem for a Nonhomogeneous Equation and explicit expressions for a generalized solution in the case of arbitrary summable $$q(x)$$ , $$\varphi (x)$$ , $$\psi (x)$$ , and $$f(x,t)$$ .
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Classical and Generalized Solutions of a Mixed Problem for a Nonhomogeneous Wave Equation
Doklady Mathematics, 2019Co-Authors: A. P. Khromov, V. V. KornevAbstract:A.N. Krylov’s ideas concerning convergence acceleration for Fourier series are used to obtain explicit expressions for the classical solution of a mixed problem for a Nonhomogeneous Equation and explicit expressions for a weak solution in the case of arbitrary summable $$q(x)$$ , $$\varphi (x)$$ , $$\psi (x)$$ , and $$f(x,t)$$ .
Meiramkul M. Amangaliyeva - One of the best experts on this subject based on the ideXlab platform.
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Spectrum of Volterra integral operator of the second kind
2016Co-Authors: Meiramkul M. Amangaliyeva, Muvasharkhan T. Jenaliyev, Madi Ergaliev, M.i. RamazanovAbstract:The article addresses the singular Volterra integral Equation of the second kind, which has the ’incompressible’ kernel. It is shown that the corresponding homogeneous Equation on |λ| ≥ exp{|arg λ|}, arg λ ∈ [−π,π] has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing |λ|. We use the Carleman-Vekua regularization method. We introduce the characteristic integral Equation. We prove that the initial integral Equation has eigen-functions, the multiplicity of which depends on the value of the spectral parameter λ. We prove the solvability theorem of the Nonhomogeneous Equation in a case when the right-hand side of the Equation belongs to a certain class.
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On the spectrum of Volterra integral Equation with the “incompressible” kernel
2014Co-Authors: Meiramkul M. Amangaliyeva, Muvasharkhan T. Jenaliyev, Minzilya T. Kosmakova, M.i. RamazanovAbstract:The article addresses the singular Volterra integral Equation of the second kind which has the “incompressible” kernel. It is shown that the corresponding homogeneous Equation for |λ| > 1 has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing |λ|. The Equation is reduced to Abel Equation by using the regularization method. The eigenfunctions of the Equation are found in an explicit form. We prove the solvability theorem of the Nonhomogeneous Equation in a case when the right-hand side of the Equation belongs to a certain class.