相关论文: Existence and uniqueness of solutions for Leontief…
We prove an existence and uniqueness result for solutions to linear $X$-elliptic equations with $L^1$ data and zero Dirichlet boundary conditions. Such solutions depend continuously on the datum. Moreover, we show that an improvement in the…
This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued…
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.
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…
Theoretical and computational properties of a vector equation $Ax-\|x\|_1x=b$ are investigated, where $A$ is an invertible $M$-matrix and $b$ is a nonnegative vector. Existence and uniqueness of a nonnegative solution is proved. Fixed-point…
We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
This paper is devoted to a nonlinear singular Riemann-Liouville type fractional differential equation, the local existence of whose continuous solutions under the weakest condition remained as an open problem until now. The singularity of…
Let $d\ge1$. Consider a stable-like operator of variable order \begin{align*} \mathcal{A}f(x) & =\int_{\mathbb{R}^{d} \backslash\{0\}} \left[f(x+h) -f(x) -\mathbf{1}_{\{|h|\le1\}}h \cdot\nabla f(x)\right]\frac{n(x,h)}{|h|^{d+\alpha(x)}}…
We discuss a stochastic interacting particles' system connected to dyadic models of turbulence, defining suitable classes of solutions and proving their existence and uniqueness. We investigate the regularity of a particular family of…
In this paper, we study the singularities of locally flat systems, motivated by the solution, if it exists, of the global motion planning problem for such systems, in the spirit of \cite{CE_14}. More precisely, flat outputs may be only…
This paper is concerned with the existence and uniqueness of positive solution for the fourth order Kirchhoff type problem $$\left\{\begin{array}{ll} u''''(x)-(a+b\int_0^1(u'(x))^2dx)u''(x)=\lambda f(u(x)),\ \ \ \ x\in(0,1),\\…
We study the existence or the nonexistence of classical solutions to a singular Gierer-Meinhardt system with Dirichlet boundary condition. The main feature of our model is that the activator and the inhibitor have different sources given by…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying…
In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.
In this note, we study the existence and uniqueness of a positive solution to a doubly singular fractional problem with nonregular data. Besides, for some cases, we will show the existence and uniqueness of another notion of a solution,…