Related papers: A variational Approach to complex Hessian equation…

A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…

We present the implementation of a variational finite element solver in the HelFEM program for benchmark calculations on diatomic systems. A basis set of the form $\chi_{nlm}(\mu,\nu,\phi)=B_{n}(\mu)Y_{l}^{m}(\nu,\phi)$ is used, where…

A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…

The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174 (2001),…

By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and…

This paper offers a new and complete description of subnormal solutions of certain non-homogeneous second order periodic linear differential equations first studied by Gundersen and Steinbart in 1994. We have established a previously…

Here is one of the results obtained in this paper: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, let $q>1$, with $q<{{n+2}\over {n-2}}$ if $n\geq 3$ and let $\lambda_1$ be the first eigenvalue of the problem $$\cases{-\Delta…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…

We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| \phi |)$ and a non-canonical kinetic term $\omega(| \phi |)…

In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega…

We prove that, in a $m$-hyperconvex domain in $\mathbb{C}^{n},$ if a non-negative Borel measure is dominated by a complex Hessian measure, then it is a complex Hessian measure of a function in the class $\mathcal{N}_m(H)$. This is an…

We develop a new generalized form of the fractional kinetic equation involving a generalized k-Bessel function. The generalized $k$-Mittag-leffler function $E^{\gamma,q}_{k,\alpha,\beta}(.)$ is discussed in terms of the solution of the…

We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum,…

We are concerned with the dynamics of $N$ point vortices $z_1,\dots,z_N\in\Omega\subset\mathbb{R}^2$ in a planar domain. This is described by a Hamiltonian system \[ \Gamma_k\dot{z}_k(t)=J\nabla_{z_k} H\big(z(t)\big),\quad k=1,\dots,N, \]…

We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. We deal with the case in which the solutions to the obstacle problems satisfy a variational…

In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by \begin{gather*} \begin{cases} -\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla…

In this paper we consider fractional quasi-Bessel equations $$\sum_{i=1}^{m}d_i x^{\alpha_i+p_i}D^{\alpha_i} u(x) + (x^\beta - \nu^2)u(x)=0$$ and construct their existence and uniqueness theory in the class of fractional series. Our…

An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal…

We use the theory of selfdual Lagrangians to give a variational approach to the homogenization of equations in divergence form, that are driven by a periodic family of maximal monotone vector fields. The approach has the advantage of using…

In this paper, we first establish the uniqueness and non-degeneracy of positive solutions to the fractional Kirchhoff problem \begin{equation*}…