Related papers: Uniqueness for linear integro-differential equatio…

In this thesis, a unified approach to prove the boundedness of gradients of solutions to degenerate and singular elliptic and parabolic phi-Laplacian systems is presented. At first, a Cacciopoli-type energy inequality with an additional…

In this note we describe how the Neumann homogenization of fully nonlinear elliptic equations can be recast as the study of nonlocal (integro-differential) equations involving elliptic integro-differential operators on the boundary. This is…

We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of…

In this article, we investigate the existence and uniqueness of a positive solution for a class of singular nonlinear elliptic problem with boundary condition. Our result holds in fractional Orlicz-Sobolev spaces.

We study the semilinear elliptic problem \[ -\Delta u = Q_{\Omega} |u|^{p-2}u \quad \text{in } \mathbb{R}^N, \] where \( Q_{\Omega} = \chi_{\Omega} - \chi_{\mathbb{R}^N \setminus \Omega} \) for a bounded smooth domain \( \Omega \subset…

We are interested in nonlocal Eikonal Equations describing the evolution of interfaces moving with a nonlocal, non monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular…

Two main results are presented: 1) a new class of applied problems that lead to equations with $(p,q)$-Laplace is presented; 2) a method for solving nonlinear boundary value problems involving $(p,q)$-Laplace with measurable unbounded…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

In this work, we study the existence, non-existence, and uniqueness results for nonlocal elliptic equations involving logarithmic Laplacian, and subcritical, critical, and supercritical logarithmic nonlinearities. The Poho\u zaev's identity…

In this paper we study Liouville-type properties for a class of degenerate elliptic equations driven by the fractional infinity Laplacian with nonlinear lower-order terms, \[ \Delta_\infty^{\beta}u - c\,H(u,\nabla u) - \lambda\, f(|x|,u)=0…

We prove existence and uniqueness results of positive viscosity solutions of fully nonlinear degenerate elliptic equations with power-like zero order perturbations in bounded domains. The principal part of such equations is either…

We consider a class of equations in divergence form with a singular/degenerate weight $$ -\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a f(x,y)+\textrm{div}(|y|^aF(x,y))\;. $$ Under suitable regularity assumptions for the matrix $A$, the forcing…

In this paper, we are concerned with Liouville-type theorems for the nonlinear elliptic equation {equation*} \Delta^2 u=|x|^a |u|^{p-1}u\;\ {in}\;\ \Omega, {equation*}where $a \ge 0$, $p>1$ and $\Omega \subset \mathbb{R}^n$ is an unbounded…

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…

We study the copolynomials of $n$ variables, i.e. $K$-linear mappings from the ring of polynomials $K[x_1,...,x_n]$ into the commutative ring $K$. We prove an existence and uniqueness theorem for a linear differential equation of infinite…

In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…

In this article we review a new method for proving the nonexistence of positive solutions of elliptic inequalities in unbounded domains in $\rn$, which was recently introduced by the authors. We expose our method and new results on the two…

The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…

In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical…

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an in- definite weight on the nonlinearity f (u, r). In particular we are interested in the case…