Related papers: Solutions to a Romanoff type problem

We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…

We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.

The paper deals with continuous solutions of a Schilling's problem.

This paper has been withdrawn, see the replacement arXiv:1302.6670.

We give a negative solution to the problem of the $L^p$-maximal regularity on various classes of Banach spaces including $L^q$-spaces with $1<q \neq 2<+\infty$.

In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the…

Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

In this short paper, we prove a Hitchin-Thorpe type inequality for closed 4-manifolds with non-positive Yamabe invariant, and admitting long time solutions of the normalized Ricci flow equation with bounded scalar curvature.

A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula.

We find wide class of exact solutions of Yang-Mills-Chern-Simons theory coupled to an external source, in terms of doubly periodic Jacobi elliptic functions. The obtained solutions include localized solitons, trigonometric solutions, pure…

We investigate existence and multiplicity of weak solutions for fourth-order problems involving the Leray-Lions type operators in variable exponent spaces and improve a result of Bonanno and Chinn\`{i} (2011). We use variational methods and…

The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…

The existence of radially symmetric solutions is discussed for a Lane-Emden type system. This answer a question posed by da Silva and do O (2024). We also comment on the inhomogeneous version of the same system and discuss some open…

We give a negative answer to a question of Bonnaf\'e on the Loewy length of a character ring of a finite group.

We propose a mechanism for solving the `negative sign problem'---the inability to assign non-negative weights to quantum Monte Carlo configurations---for a toy model consisting of a frustrated triplet of spin-$1/2$ particles interacting…

Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…

This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…

We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.

Under appropriate spectral assumptions we prove two existence results for positive solutions of Lichnerowicz-type equations on complete manifolds. We also give a priori bounds and a comparison result that immediately yields uniqueness for…