Related papers: On some variational algebraic problems
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We discuss the existence, non-existence and multiplicity of nontrivial solutions for systems of Caputo fractional differential equations subject to nonlocal boundary conditions. Our methodology relies on classical fixed point index and we…
We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…
We investigate a class of nonlinear nonautonomous scalar field equations with fractional diffusion, critical power nonlinearity and a subcritical term. The involved potentials are allowed for vanishing behavior at infinity. The problem is…
We consider a class of pseudo-relativistic Hartree equations in presence of general nonlinearities not satisfying the Ambrosetti-Rabinowitz condition. Using variational methods based on critical point theory, we show the existence of two…
We discuss the existence of solutions of nonlinear problem involving,two critical Sobolev exponents. we will ll out the su cient conditions to nd solutions for the problem in presence of a nonlinear Neumann boundary data with a critical…
We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three nonzero solutions. When the reaction term is sublinear at infinity, we apply the second…
We prove new results on the existence, non-existence, localization and multiplicity of nontrivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to nonlocal, nonlinear, functional boundary…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
In this paper, we introduce the notion of variational free boundary problem. Namely, we say that a free boundary problem is variational if its solutions can be characterized as the critical points of some shape functional. Moreover, we…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…
In this paper we prove the existence of infinitely many nontrivial solutions for the class of $(p,\, q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in $\mathbb{R}^N$. Further, when the…
We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…