Related papers: Ambrosetti-Rabinowitz theorems revisited

We introduce a wide class of deterministic subsets of primes of zero relative density and we prove Roth's Theorem in these sets, namely, we show that any subset of them with positive relative upper density contains infinitely many…

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…

We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass…

This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel in the full space. We derive a critical mass threshold below which global existence is ensured. Using carefully energy…

The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…

In a recent paper, the first author provided some lower bounds to solutions of the equations of Fermat and Catalan, based on local power series developments at the ramified prime of a prime cyclotomic extension. Although both equations have…

Below we establish the conditions guaranteeing the reality of all the zeros of polynomials $P_n(z)$ in the polynomial sequence $\{P_n(z)\}_{n=1}^{\infty}$ satisfying a five-term recurrence relation $$P_{n}(z)= zP_{n-1}(z) + \alpha…

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems involving the (p(x), q(x))-equation and the nonlinearity is superlinear but does not satisfy the usual…

It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations. To investigate this, we study the Born-Infeld scalar in two spacetime dimensions.…

In this note we deduce a strengthening of the Orlicz-Pettis theorem from the It\^o-Nisio theorem. The argument shows that given any series in a Banach space which isn't summable (or more generally unconditionally summable), we can construct…

In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev…

We consider the energy critical nonlinear Schrodinger equation on generic irrational tori. Using the long-time Strichartz estimates proved in [8], we establish polynomial upper bounds for higher Sobolev norms for solutions with small…

The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…

We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient…

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equivalent to the solvability of an associated multi- time…

It is well known that the strong subadditivity theorem is hold for classical system, but it is very difficult to prove that it is hold for quantum system. The first proof of this theorem is due to Lieb by using the Lieb's theorem. Here we…

The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Brenier's theorem and the Kantorovich-Rubinstein formula are…

Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in…

We are concerned with a super-Liouville equation on compact surfaces with genus larger than one, obtaining the first non-trivial existence result for this class of problems via min-max methods. In particular we make use of a Nehari manifold…