Related papers: Exact Solutions for the Singularly Perturbed Ricca…

In this article, we study the quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms. We quantify the strong unique continuation property by estimating the maximal vanishing order of…

We obtain uniqueness and existence of a solution $u$ to the following second-order stochastic partial differential equation (SPDE) : \begin{align} \label{abs eqn} du= \left( \bar a^{ij}(\omega,t)u_{x^ix^j}+ f \right)dt + g^k dw^k_t, \quad t…

This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear fractional differential equation with mixed boundary value conditions. Riemann-Liouville fractional derivative is considered. An…

We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose nonlinear drift parts are sums of the sub-differential of a convex function and a bounded part. This…

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under some mild assumptions and the framework of the…

In this paper we study the uniqueness property of solutions to the steady incompressible Euler equations with perturbations in $\Bbb R^N$. Our perturbations include as special cases the Euler equations with a `single signed' nonlinear term,…

We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…

In this article, we investigate the existence and uniqueness of a positive solution for a class of singular nonlinear elliptic problem with boundary condition. Our result holds in fractional Orlicz-Sobolev spaces.

In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1},…

A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed…

The purpose of this work is to analyze the wellposedness and the blow-up of solutions of the higher-order parabolic semilinear equation \[ u_t+(-\Delta)^{d}u=|x|^{\alpha}|u|^{p}+\zeta(t){\mathbf w}(x) \ \quad\mbox{for }…

Let $ \{d_q, \Lambda^{q} \} $ be de Rham complex on a smooth compact closed manifold $X$ over $ \mathbb{R}^3 $ with Laplacians $\Delta_{q} $. We consider operator equations, associated with the parabolic differential operators $\partial_t +…

We prove the existence of a positive {\it SOLA (Solutions Obtained as Limits of Approximations)} to the following PDE involving fractional power of Laplacian \begin{equation} \begin{split} (-\Delta)^su&= \frac{1}{u^\gamma}+\lambda…

In this paper we study the existence and uniqueness of a solution and propose an iterative method for solving a beam problem which is described by the fully fourth order equation $$u^{(4)}(x)=f(x,u(x),u'(x),u'''(x),u'''(x)), \quad 0 < x <…

In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…

We establish, for the first time, explicit a priori and regularity estimates for solutions of the Dirichlet problem for Hamilton-Jacobi-Bellman operators from stochastic control, whose principal half-eigenvalues have opposite signs. In…

We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic…

We show the existence, regularity and analyticity of solitary waves associated to the following equation \begin{eqnarray*} (u_t+u^{p}u_x+ \mathcal H\partial_x^2u+ \lambda \mathcal H\partial_y^2u)_x +\mu u_{yy}=0, \end{eqnarray*} where…

We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla u}{(1+u)^{\theta(p-1)}}\right) = h(u)f…

We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati--Pad\'e method that is based on a rational approximation to a regularized logarithmic derivative of the wavefunction. Sequences of roots of Hankel…