Related papers: Existence, Uniqueness and Removable Singularities …
We construct positive weak solutions of a class of semilinear elliptic equation which vanish in suitable trace sense on the boundary of a given smooth bounded N-dimensional domain, but which are singular at prescribed isolated points of the…
We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.
The main objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order $\sigma\in(1,2),$…
A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains valid, if the area functional is replaced by a general…
On a Riemannian manifold with a smooth function $f: M\to \mathbb{R}$, we consider the linearization of the Perelman scalar curvature $\mathcal{R}$ and its $L^2$-formal adjoint operator $\delta\mathcal{R}^*$. A manifold endowed with a metric…
We consider a system of quasilinear elliptic equations, with indefinite super-linear nonlinearity, depending on two real parameters $\lambda,\mu$. By using the Nehari manifold and the notion of extremal parameter, we extend some results…
This paper introduces the concept of renormalized solution for a general class of non-coercive nonlinear parabolic problems, including both singularities and unbounded lower order terms. We prove existence and uniqueness of renormalized…
In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…
In the Painleve analysis of nonintegrable partial differential equations one obtains differential constraints describing the movable singularity manifold. We show, for a class of n-dimensional wave equations, that these constraints have a…
We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is $$\begin{cases} -\Delta_p u = H(u)\mu & \text{in}\ \Omega,\\ u>0…
In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
We establish uniqueness results for quasilinear elliptic problems through the criterion recently provided in \cite{DFMST}. We apply it to generalized $p$-Laplacian subhomogeneous problems that may admit multiple nontrivial nonnegative…
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…