Related papers: A note on Blasius type boundary value problems
We give a uniform estimate and an inequality for solutions of an equation with Dirichlet boundary condition.
Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or…
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with…
We calculate the full asymptotic expansion of boundary blow-up so- lutions, for any nonlinearity f . Our approach enables us to state sharp qualitative results regarding uniqueness and ra- dial symmetry of solutions, as well as a…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.
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.
We prove global existence and blow-up of solutions of initial-boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in…
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear $p$-Laplace equations in Euclidean space by showing symmetry and uniqueness of positive solutions to associated limiting problems.
We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singularities. The result is motivated by our recent partial…
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We…
In this paper, we discuss differentiation of solutions to the boundary value problem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\; y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and $y^{(i)}(x_k) +…
A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…