相关论文: On solvability of nonlinear partial differential s…
We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As…
We prove a general local existence theorem for nonlinear systems of Cauchy-Riemann operator of any order in one complex variable with initial values at a given point, which is a counterpart of local existence of ODE.
We present a general existence proof for a wide class of non-linear elliptic equations which can be applied to problems with barrier conditions without specifying any assumptions guaranteeing the uniqueness or local uniqueness of particular…
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.
This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
We give a new proof of the existence (\cite{HM}, \cite{Ren}) of a Jenkins-Strebel differential $\Phi$ on a Riemann surface $\SR$ with prescribed heights of cylinders by considering the harmonic map from $\SR$ to the leaf space of the…
We study a particular system of partial differential equations in which the harmonic, the divergence and the gradient operators of the unknown functions appear (harmonic-divgrad system). Using the Killing Hopf theorem and leveraging the…
We extend Halphen's theorem which characterizes the solutions of certain $n$th-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order $n \times n$ system of differential equations. As an…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
The classical Julia-Wolff-Caratheodory theorem gives a condition ensuring the existence of the non-tangential limit of both a bounded holomorphic function and its derivative at a given boundary point of the unit disk in the complex plane.…
We obtain sufficient conditions ensuring the existence of a uniformly continuous and H\"older continuous homeomorphism between the solutions of a linear system of differential equations with piecewise constant argument of generalized type…
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…
We discuss the solvability of an infinite system of first order ordinary differential equations on the half line, subject to nonlocal initial conditions. The main result states that if the nonlinearities possess a suitable "sub-linear"…
We survey several results in value distribution theory for parabolic Riemann surfaces. Let Y be a parabolic Riemann surface, i.e. subharmonic functions defined on Y are constant. We discuss Nevanlinna's theory for holomorphic maps f from Y…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In this paper, we establish a result for existence and uniqueness of stochastic differential equations on Riemannian manifolds, for regular inhomogeneous tensor coefficients with stochastic drift, under geometrical hypothesis on the…
We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.