Related papers: The Ljapunov-Schmidt reduction for some critical p…
We obtain nontrivial solutions of a critical fractional $p$-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving…
In this work we study the following fractional critical problem $$ (P_{\lambda})=\left\{\begin{array}{ll} (-\Delta)^s u=\lambda u^{q} + u^{2^*_{s}-1}, \quad u{>}0 & \mbox{in} \Omega\\ u=0 & \mbox{in} \RR^n\setminus \Omega\,,…
We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear systems with pure imaginary spectrum and may be generalized to…
We give a blow-up behavior for solutions to a problem with singularity and with Dirichlet condition. An application, we have a compactness of the solutions to this Problem with singularity and Lipschitz conditions.
In this paper, we investigate critical quasilinear elliptic partial differential equations on a complete Riemannian manifold with nonnegative Ricci curvature. By exploiting a new and sharp nonlinear Kato inequality and establishing some…
We consider singular perturbation elliptic problems depending on a parameter ? such that, for ? = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit only holds in…
We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem.
We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial…
For a broad class of nonlinear systems, we construct smooth control-Lyapunov functions whose derivatives along the trajectories of the systems can be made negative definite by smooth control laws that are arbitrarily small in norm. We…
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
Jellium correction on the fissionability parameter is estimated within a Liquid Drop Model of the charged metallic cluster. This correction modifies the critical condition of fission and, it becomes relevant for small multicharged clusters.
Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is…
Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…
The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
In this paper, we investigate the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary. The existence result is assured under some geometric conditions.
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…