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Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations
We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type)...
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Uniqueness and Non-Uniqueness Results for Forced Dyadic MHD Models
We construct non-unique Leray–Hopf solutions for some forced dyadic models for magnetohydrodynamics (MHD) when the intermittency dimension
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Uniqueness of continuation for semilinear elliptic equations
We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case....
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Uniqueness and Structure of Solutions
This Chapter is devoted to the study of uniqueness and structure of solutions to the anisotropic least gradient problem. As we saw in Chaps. 1 and...
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Uniqueness of weak solutions of the Plateau flow
In this paper, we study the uniqueness of weak solutions of the heat flow of half-harmonic maps, which was first introduced by Wettstein as a...
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Uniqueness in Regularity and Dirichlet Problems
This chapter complements Chaps. 17 , 18 and 19...
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Weak-strong uniqueness for three dimensional incompressible active liquid crystals
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models. In this...
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Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise
We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system that is forced by random noise of an additive and a linear...
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Uniqueness theorems for weighted harmonic functions in the upper half-plane
We consider a class of weighted harmonic functions in the open upper half-plane known as α -harmonic functions. Of particular interest is the...
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Nontrivial Solutions for the Polyharmonic Problem: Existence, Multiplicity and Uniqueness
The authors consider the existence, multiplicity, and uniqueness for polyharmonic problem with Navier boundary conditions. One of the interesting...
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Existence and Uniqueness Theorems for the Pfaff Equation with Continuous Coefficients
In this paper, the Pfaff equations with continuous coefficients are considered. Analogs of Peano’s existence theorem and Kamke’s theorem on the...
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Jordan-Hölder Theorem with Uniqueness for Semimodular Lattices
In 2011 Czédli and Schmidt proved the strongest form of Jordan-Hölder theorem for lattices, which they called Jordan-Hölder theorem with uniqueness:...
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Set of Uniqueness for Cantorvals
The main result is that the celebrated Guthrie–Nymann’s Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager...
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A Nagumo-Type Uniqueness Criterion for a Differential Equation with Convolution
In this note we present a uniqueness result of Nagumo type for an initial value problem depending on a convolution. An illustrative example is...
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Uniqueness of Constant Mean Curvature Spheres
We survey on the problem of finding all constant mean curvature two-spheres inside a given ambient Riemannian three-manifold. While this task is...
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Uniqueness Functions to Conformable Differential Inclusions
We study conformable evolution inclusions with the help of uniqueness (Perron) functions. Our conditions are much weaker than commonly used Lipschitz...
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On the Uniqueness of Continuation for Polynomials of Harmonic Quaternion Fields
The paper provides a counterexample to the hypothesis on the uniqueness of continuation for polynomials of harmonic quaternion fields in a compact...
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Positive Solutions for Biharmonic Equations: Existence, Uniqueness and Multiplicity
The primary objective of this article is to consider a class of biharmonic equations with Navier boundary conditions. Among others, a new criterion...