相关论文: Solutions for a class of iterated singular equatio…
We give some estimate of type sup*inf for scalar curvature type equations.
We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The construction is performed by studying the asymptotics of…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator…
In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of…
We consider radially symmetric solutions for a class of resonant problems on a unit ball $B \subset R^n$ around the origin \[ \Delta u+\la _1 u +g(u)=f(r) \s \mbox{for $x \in B$}, \s u=0 \s \mbox{on $\partial B$} \,. \] Here the function…
We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi-Yau type problems in torus bundles.
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before…
We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.
In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative.…
We study elliptic families of solutions to the recently introduced constrained Toda hierarchy, i.e., solutions which are elliptic functions of some linear combination of the hierarchical times. Equations of motion for poles of such…
We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.
By using truncation technique, minimization method and Morse theory, we obtain three nontrivial solutions for a class of semilinear elliptic equations.
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
We study the existence of singular separable solutions to a class of quasilinear equations with reaction term. In the 2-dim case, we use a dynamical system approach to construct our solutions.
We review elliptic solutions to integrable nonlinear partial differential and difference equations (KP, mKP, BKP, Toda) and derive equations of motion for poles of the solutions. The pole dynamics is given by an integrable many-body system…