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Related papers: On singular Abreu equations in higher dimensions

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We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.

Complex Variables · Mathematics 2020-04-10 Dinesh Kumar , Sanjay Kumar , Manisha Saini

The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…

Analysis of PDEs · Mathematics 2024-07-16 Mehmet Erbay , Birgit Jacob , Kirsten Morris

We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…

Algebraic Geometry · Mathematics 2016-08-09 Szilard Szabo

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

Rings and Algebras · Mathematics 2014-01-14 Ivan Shestakov , Maria Trushina

In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric…

Analysis of PDEs · Mathematics 2007-05-23 Yue He

In this paper, we consider radial distributional solutions of the quasilinear equation $-\Delta_N u=f(u)$ in the punctured open ball $ B_R\backslash\{0\}\subset \RR^N$, $N \geq 2$. We obtain sharp conditions on the nonlinearity $f$ for…

Analysis of PDEs · Mathematics 2018-07-17 M. Ghergu , J. Giacomoni , S. Prashanth

We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We…

Complex Variables · Mathematics 2013-07-31 Samuele Mongodi , Alberto Saracco

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…

Classical Analysis and ODEs · Mathematics 2008-12-19 Yifei Pan , Mei Wang

The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs…

Analysis of PDEs · Mathematics 2009-11-13 Nikolai Dokuchaev

It is studied the Hilbert boundary value problem for the nondegenerate Beltrami equations in domains $D$ of the complex plane $\mathbb C$ with the so--called quasihyperbolic boundary condition. It is proved the existence of solutions of…

Complex Variables · Mathematics 2019-11-22 V. Gutlyanskii , V. Ryazanov , E. Yakubov , A. Yefimushkin

We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity…

Exactly Solvable and Integrable Systems · Physics 2011-08-24 James Atkinson , Nalini Joshi

This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…

Classical Analysis and ODEs · Mathematics 2025-06-23 Shalmali Bandyopadhyay , Kyle Byassee , Curt Lynch

Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.

Classical Analysis and ODEs · Mathematics 2012-11-16 Ryu Sasaki , Kouichi Takemura

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…

Classical Analysis and ODEs · Mathematics 2010-01-25 Douglas R. Anderson

In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…

Functional Analysis · Mathematics 2009-10-06 Rustamova Lamiya Aladdin

We investigate the boundedness of solutions of the first order linear difference equation of the form $x_{n+1} = Ax_{n} + y_{n}, \; n \geq 1$ where $A$ is a square matrix with complex entries, sequence $\{y_{n}\}_{n\geq 1}$ and initial…

Dynamical Systems · Mathematics 2025-09-23 Andrii Chaikovskyi , Oleksandr Liubimov

We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory.

Classical Analysis and ODEs · Mathematics 2013-07-17 Mikolaj Peplonski

We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit

In this paper the concept of measure of noncompactness is applied to prove the existence of solution for a boundary value problem for an infinite system of second order differential equations in $\ell_{p}$ space. We change the boundary…

Functional Analysis · Mathematics 2018-07-17 Ishfaq Ahmad Malik , Tanweer Jalal

We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an…

General Relativity and Quantum Cosmology · Physics 2012-09-06 Ellery Ames , Florian Beyer , James Isenberg , Philippe G. LeFloch