Related papers: Carleman-Vekua equation with a singular point
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the $k$-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of…
We give a blow-up analysis and a compactness result for an equation with Holderian condition and boundary singularity.
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori $C^2$ estimates for $(k-1)$-admissible solutions in almost convex and uniformly $(k-1)$-convex domains, and prove the existence of…
In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…
We study mean field equations with singular sources on a compact Riemann surface with boundary $(\Sigma,g)$, subject to homogeneous Neumann boundary conditions: \[ -\Delta_g v = \rho\left( \frac{V e^{v}}{\int_\Sigma V e^{v}\, d v_g} -…
We give two distinct infinite-Hamiltonian representations for the Riemann equation. One with first order Hamiltonian operators and another with third order-first order Hamiltonian operators. Both representations contain an arbitrary…
In this paper,for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get…
In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert…
In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…
The purpose of this article is two-fold. First, we investigate the inequality $$ -\Delta u+V(x) u\geq f\quad\mbox{ in } B_1\setminus\{0\}\subset \mathbb{R}^N , N \geq 2, $$ where $f\in L^1_{loc}(B_1)$. If $V\geq 0$ is radially symmetric, we…
We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying \[ 0\le-\Delta_{p}u(x)\le \tau u^{\frac{n(p-1)}{n-p}} (x),\,\,u(x)\ge0,\,\,1<p<n,\,\,n\ge2, \]where $u(x)\in…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
The generalized CR equation $u_{\bar{z}}=au+b\bar{u}+f$ is studied when the coefficients $a$ and $b$ have a finite number of singular points inside the domain. Solutions are constructed via the study of an associated integral operator and…
We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb…
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…
The initial-boundary value problem for the Kundu--Eckhaus equation on the half-line is considered in this paper by using the Fokas method. We will show that the solution $u(x,t)$ can be expressed in terms of the solution of a matrix…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
The focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH) problem. We derive some new results for the…