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Correction to: On the Unique Solvability of the Absolute Value Equation
In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory...
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Unique Solvability of the Zaremba Problem for Linear Second Order Elliptic Equations with Drift
We establish the unique solvability of the Zaremba problem for linear second order elliptic equations in divergence form with measurable coefficients...
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Characterization of unique solvability of absolute value equations: an overview, extensions, and future directions
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In...
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Unique Solvability of the Boundary-Value Problems for Nonlinear Fractional Functional Differential Equations
By using the Krasnoselskii theorem, we obtain general conditions for the unique solvability of boundaryvalue problems for (non)linear fractional...
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Absolute Value Equations with Tensor Product Structure: Unique Solvability and Numerical Solution
We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail:...
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On the Unique Solvability of Boundary Value Problems for an Abstract Euler–Poisson–Darboux Equations on a Finite Interval
AbstractSufficient conditions for the unique solvability of boundary value problems for a number of abstract singular equations that are formulated...
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On the Unique Solvability of Initial–Boundary Value Problems for Parabolic Systems in Bounded Plane Domains with Nonsmooth Lateral Boundaries
AbstractWe consider the first and second initial–boundary value problems for inhomogeneous second-order parabolic systems with Dini continuous...
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Unique Solvability and Non-uniqueness in the Problem of Forward Motion of Bodies in a Two-Layer Fluid
The classical ship-wave problem, describing forward motion of rigid bodies with a constant speed in an unbounded heavy fluid having a free surface,...
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Errata of the Unique Solvability of the Absolute Value Equation
A published counterexample motivates us to correct one of our theorems in the previously published work in Wu and Guo (J Optim Theory Appl...
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To a Unique Solvability of a Problem with Integral Condition for Integro-Differential Equation
AbstractProblem with integral condition for Fredholm integro-differential equation is considered. Conditions for a unique solvability of problem with...
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Unique solvability of weakly homogeneous generalized variational inequalities
An interesting observation is that most pairs of weakly homogeneous map**s do not possess strongly monotonic property, which is one of the key...
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On the Solvability of Linear Differential Operators on Vector Bundles over a Manifold
AbstractA necessary and sufficient condition is established for the closedness of the range or surjectivity of a differential operator acting on...
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Local Unique Solvability of a Quasilinear Equation with the Dzhrbashyan–Nersesyan Derivatives
AbstractThe existence of a unique local solution for an initial problem to a quasilinear equation in a Banach space with the Dzhrbashyan–Nersesyan...
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On the Unique Solvability of a Boundary Value Problem for Systems of Loaded Integro-Differential Equations with Involution
AbstractIn this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory...
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Solvability of Linear Differential Equations
AbstractWe propose a new approach to the solvability of ordinary as well as partial differential equations in the theory of linear differential...
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Unique Solvability of Direct and Inverse Problems for Degenerate Parabolic Equations in the Multidimensional Case
We study the inverse problem of recovering the source function in a degenerate parabolic equation with many spatial variables. An additional integral...
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On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations
AbstractIn a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann boundary value problems for a functional-differential...
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On the Solvability of Boundary Value Problems for an Abstract Singular Equations on a Finite Interval
AbstractSufficient conditions for the unique solvability of boundary value problems for a number of abstract singular equations that are formulated...
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Solvability of the Generalized Ionkin Problem for Differential Equations with Multiple Characteristics
We study the solvability of nonlocal spatial boundary value problems with generalized Samarskii–Ionkin condition. We prove the existence and...
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On the Solvability of Heat Boundary Value Problems in Sobolev Spaces
AbstractIn a domain, degenerating into a point at the initial moment of time, we consider a boundary value problem (BVP) of heat conduction that is a...
