相关论文: Critical elliptic equations on non-compact Finsler…
In this paper, we show the existence of non-trivial solutions to very general elliptic systems with critical non-linearities in the sense of embeddings in Orlicz-Sobolev spaces. This allows to consider non-linearities which do not have…
In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order $s \in (0,1)$. We identify minimal conditions on the nonlinear term and the source which leads to existence of…
We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain $\Omega\subset \>I\!\!R^{N}\>(N…
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.
Given a complete non-compact Riemannian manifold $(M,g)$ with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries $G$ of $(M,g)$ that characterizes the coerciveness of $G$ in the sense of…
This paper is concerned with a biharmonic equation under the Navier boundary condition with nearly critical exponent. We study the asymptotic behavior os solutions which are minimizing for the Sobolev quatient. We show that such solutions…
It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…
This paper aims to establish counterparts of fundamental regularity statements for solutions to elliptic equations in the setting of low-dimensional structures such as, for instance, glued manifolds or CW-complexes. The main result proves…
The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…
The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -{\Delta}_{p}u={\lambda}k(x)u^{q}\pmh(x)u^{{\sigma}} if x\in{\Omega}, subject to the Dirichlet conditions…
In this paper, we are concerned with the following elliptic equation $$ ( SC_\varepsilon ) \qquad \begin{cases} -\Delta u = |u|^{4/(n-2)}u [\ln (e+|u|)]^\varepsilon & \hbox{ in } \Omega,\\ u = 0 & \hbox{ on }\partial \Omega, \end{cases} $$…
We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak…
The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on…
In this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of Kirchhoff type. Due to the degeneration of the nonlocal term it is not possible to…
In this work, we prove the existence of least energy nodal solution for a class of elliptic problem in both cases, bounded and unbounded domain, when the nonlinearity has exponential critical growth in $\mathbb{R}^2$. Moreover, we also…
The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we…
We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…
This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…