Related papers: A Note on the Paper "The unique solution of the ab…

We consider semilinear elliptic equations with double power nonlineaities. The condition to assure the existence of positive solutions is well-known. In the present paper, we remark that the additional condition to assure uniqueness…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

The main purpose of this Note is to provide a non-trivial bound on certain Kloosterman sums as considered in the recent paper of E. Fouvry [F], leading to a small improvement of his result on the Pell equation.

In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic…

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].

In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher powers.

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

We comment that the conditionally exactly solvable potential of Dutt et al. and the exactly solvable potential from which it is derived form a dual system.

Exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the…

In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.

In this addendum note we fill in the gap left in \cite{ls} in the description of 2D homogeneous solutions to the stationary Euler system with the help of the results of \cite{sd}. This gives a complete classification of all solutions. The…

We consider an open question posed in \cite{Zhu-Baggio-17} on the uniqueness of the solution to a parametric spectral estimation problem.

We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr. [7] they have…

This note is intended to explain the proof of two facts about quadrature domains: first, they are essentially unique if they exist; and second, they do exist for a large class of weight functions. The proofs roughly follow Sakai's…

We prove existence and uniqueness of distributional, bounded, nonnegative solutions to a fractional filtration equation in ${\mathbb R}^d$. With regards to uniqueness, it was shown even for more general equations in [19] that if two bounded…

This paper gives a new perspective on how to solve the second-order linear differential equation written in normal form. Extending the argument of the potential to a complex number leads to solving exactly the Schr\"odinger equation when…

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

In a recent paper [3], Bakalov and Milanov proved that the total descendant potential of a simple singularity satisfies the W-constraints, which come from the W-algebra of the lattice vertex algebra associated to the root lattice of this…

Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle…

We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give several applications, arising in both mathematics and…