相关论文: On some abstract version of the Cauchy-Kowalewski …
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
This expository paper focuses on free Lie $K$-algebras and the basic PBW theorem. We argue in various ways that the basic PBW theorem is a quite close consequence of the Magnus-Witt theorems concerning free Lie algebras.
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
The Cauchy problem is studied for systems of quasi-linear wave equations with multiple speeds in two space dimensions. Using the method of Klainerman and Sideris together with the localized energy estimate, we give an alternative proof of a…
We carry out an investigation of the existence of infinitely many solutions to a fractional $p$-Kirchhoff type problem with a singularity and a superlinear nonlinearity with a homogeneous Dirichlet boundary condition. Further the…
A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required…
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof…
In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact…
In this work we proivied a new simpler proof of the global diffeomorphism theorem from [9] which we further apply to consider unique solvability of some abstract semilinear equations. Applications to the second order Dirichlet problem…
We analyze the Cauchy problem for symmetric hyperbolic equations with a time singularity of Fuchsian type and establish a global existence theory along with decay estimates for evolutions towards the singular time under a small initial data…
We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\cdot)$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\cdot)\in (\inf p,\sup p)$. This setting leads to…
We establish an abstract critical point theorem for locally Lipschitz functionals that does not require any compactness condition of Palais-Smale type. It generalizes and unifies three other critical point theorems established in…
We study the Cauchy problem for an inhomogeneous Gross-Pitaevskii equation. We first derive a sharp threshold for global existence and blow up of the solution. Then we construct and classify finite time blow up solutions at the minimal mass…
A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.
Using H\"{o}rmander $L^2$ method for Cauchy-Riemann equations from complex analysis, we study a simple differential operator $\bar{\partial}^k+a$ of any order (densely defined and closed) in weighted Hilbert space…
The objective of this article is to prove the necessity statement in Crawley-Boevey's conjectural solution to the (tame) Deligne-Simpson problem. We use the nonabelian Hodge correspondence, variation of parabolic weights and results of…
In this paper we consider the following Cauchy problem for the semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity: \begin{align}\label{CP abstract} \begin{cases} u_{tt}-\Delta u+\dfrac{\mu_1}{1+t}…
We prove a local-in-time existence and uniqueness theorem for a smooth classical solution to the spatially homogeneous Boltzmann equation with cutoff soft potentials. Our proof is based on a series of bilinear estimates for the…
This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz…
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is…