Related papers: Remarks on the Clark theorem

We argue that there exists an infinite class of conformal field theories in diverse dimensions, having a universal ratio of the central charge c to the normalized entropy density c'. The universality class includes all conformal theories…

In this paper, we study the existence and nonexistence of positive solutions for a coupled elliptic system with critical exponent and logarithmic terms. The presence of the the logarithmic terms brings major challenges and makes it…

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this…

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this…

Given two elementary embeddings from the collection of sets of rank less than $\lambda$ to itself, one can combine them to obtain another such embedding in two ways: by composition, and by applying one to (initial segments of) the other.…

Let $\Omega$ be a bounded domain in $\mathbb R^{N}$, $N\geq3$ with smooth boundary, $a>0, \lambda>0$ and $0<\delta<3$ be real numbers. Define $2^*:=\displaystyle\frac{2N}{N-2}$ and the characteristic function of a set $A$ by $\chi_A$. We…

We discuss the existence and non-existence of non-negative weak solutions for second order nonlocal elliptic systems subject to functional boundary conditions. Our approach is based on classical fixed point index theory combined with some…

We establish direct evidence of the arithmetic significance of plectic Stark-Heegner points for elliptic curves of arbitrarily large rank. The main contribution is a proof of the algebraicity of plectic points associated to polyquadratic CM…

We establish for smooth projective real curves the equivalent of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

The Riemann Hypothesis is a conjecture that all non-trivial zeros of Riemann Zeta function are located on the critical line in the complex plane. Hundreds of propositions in function theory and analytic number theory rely on this…

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter.…

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between…

Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps…

In this paper we prove the existence of a positive solution of the nonlinear and nonlocal elliptic equation in $\mathbb{R}^n$ \[ (-\Delta)^s u =\varepsilon h u^q+u^{2_s^*-1} \] in the convex case $1\leq q<2_s^*-1$, where $…

The main purpose of this paper is to establish the existence of positive solutions to a class of quasilinear elliptic equations involving the (p-q)-Laplacian operator. We consider a nonlinearity that can be subcritical at infinity and…

We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem,…

The Endpoint Theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It…

We suggest a tetracritical fixed point to naturally occur in strongly interacting theories. As a fundamental example we analyze the temperature--quark chemical potential phase diagram of QCD with fermions in the adjoint representation of…

Critical phenomena have been extensively investigated both theoretically and experimentally in many fields, such as condensed matter physics, biology, e.g., brain criticality, and cosmology. In particular, the behaviour of response…

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…