Related papers: Nonlinear differential equations on non-compact do…
In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for linear equations. The geometrical conditions in this paper are…
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
The present work has two objectives. First, we prove that a weight\-ed superlinear elliptic problem has infinitely many nonradial solutions in the unit ball. Second, we obtain the same conclusion in annuli for a more general nonlinearity…
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…
We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.
In this paper, the exact solutions of certain non-linear differential equations defined on a fractal subset of the real line are presented. Particular attention is paid to the Riccati-type fractal differential equation, for which a…
We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.
We construct solutions to p-Laplace type equations in unbounded Lipschitz domains in the plane with prescribed boundary data in appropriate fractional Sobolev spaces. Our approach builds on a Cauchy integral representation formula for…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
In this paper, we establish pointwise boundary ${{C}^{1,\alpha}}$ estimates for viscosity solutions of some degenerate fully nonlinear elliptic equations on ${C^{1,\alpha}}$ domains. Instead of straightening out the boundary, we utilize the…