Related papers: Regularity of the extremal solutions in a Gelfand …
We start with some global Maxwellian function $M$, which is a stationary solution (with the constant total density $\rho$) of the Boltzmann equation, and we denote the number of the corresponding space variables by $n$. The notion of…
We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic…
We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…
The boundedness of stable solutions to semilinear (or reaction-diffusion) elliptic PDEs has been studied since the 1970's. In dimensions 10 and higher, there exist stable energy solutions which are unbounded (or singular). This note…
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
We consider an elliptic system with regular H{\"o}lderian weight and exponential nonlinearity or with weight and boundary singularity, and, Dirichlet condition. We prove the boundedness of the volume of the solutions to those systems on the…
We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
Let $X=\mathbb{D}/\Gamma$ be an arbitrary Riemann surface. We establish a necessary and sufficient criterion for $[f]\in T(X)$ to have a Teichm\"uller-type extremal map.
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of…
We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial…
We are concerned with the existence and boundary behaviour of positive radial solutions for the system \begin{equation*} \left\{ \begin{aligned} \Delta u&=|x|^{a}v^{p} &&\quad\mbox{ in } \Omega, \\ \Delta v&=|x|^{b}v^{q}f(|\nabla u|)…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…