Related papers: On continuous solutions of a problem of R.Schillin…
In this paper, we consider the Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds. Under the assumption of an admissible subsolution, we solve the existence and the uniquness for the Dirichlet problem in a…
In this paper, we study the residual solvability of the generalized free product of solvable groups.
The aim of this paper is twofold. First, we establish the representation formula and the uniqueness of the solutions to a class of inhomogeneous biharmonic Dirichlet problems, and then prove the bi-Lipschitz continuity of the solutions.
Global regular axially symmetric solutions with large swirl in a cylinder with periodic conditions on the top and on the bottom are proved. On the lateral part of its boundary the boundary slip conditions are assumed. The proof is obtained…
There is studied problem on solvability of linear non-homogeneous differential equation of higher even order. There is proved the theorem on necessary and sufficient conditions on existence of solutions to the equation in the Schwartz…
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
An English summary is given of Jean Delsarte's article "Nombre de solutions des equations polynomiales sur un corps fini."
The aim of this paper is analyzing existence, multiplicity, and regularity issues for the positive solutions of a Neumann boundary value problem of superlinear indefinite type related to the mean curvature operator with a sublinear…
This paper is concerned with the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u- \Delta(u^2)u =h(u), \ \ \mbox{in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$. Under appropriate assumptions on $V$ and $h$, we…
We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in…
In this paper we first obtain the existence of smooth solutions to Orlicz-Aleksandrov problem via a Gauss-like curvature flow.
We obtain existence and multiplicity results for quasilinear fourth order elliptic equations on $\mathbb{R}^{N}$ with sign-changing potential. Our results generalize some recent results on this problem.
A local behavior of solutions of the Schlesinger equation is studied. We obtain expansions for this solutions, which converge in some neighborhood of a singular point. As a corollary the similar result for the sixth Painlev\'e equation was…
We give a sharp estimate of the modulus of continuity of the solution to the Dirichlet problem for the complex Hessian equation of order $m$ ($1 \leq m \leq n$) with a continuous right hand side and a continuous boundary data in a bounded…
The paper deals with the Dirichlet problem for the nonstationary Stokes system in a cone. The authors obtain existence and uniqueness results for solutions in weighted Sobolev spaces and study the asymptotics of the solutions at infinity.
We examine a Gelfand type system and show the extremal solutions are bounded provided we are close enough to the scalar case.
This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen…
We consider the existence and multiplicity of solutions for a class of quasi-linear Schr\"{o}dinger equations which include the modified nonlinear Schr\"{o}dinger equations. A new perturbation approach is used to treat the sub-cubic…