Results 1 to 10 of about 37,919 (260)
Polynomial Solutions of Equivariant Polynomial Abel Differential Equations [PDF]
Advanced Nonlinear Studies, 2018 Let a(x){a(x)} be non-constant and let bj(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a(x)y˙=b1(x)y+b3(x)y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
doaj +9 more sources
Trigonometric Polynomial Solutions of Bernoulli Trigonometric Polynomial Differential Equations
Mathematics, 2022 We consider real trigonometric polynomial Bernoulli equations of the form A(θ)y′=B1(θ)+Bn(θ)yn where n≥2, with A,B1,Bn being trigonometric polynomials of degree at most μ≥1 in variables θ and Bn(θ)≢0.
Claudia Valls
doaj +2 more sources
Mathematics, 2020 We study equations of the form y d y / d x = P ( x , y ) where P ( x , y ) ∈ R [ x , y ] with degree n in the y-variable. We prove that this ordinary differential equation has at most n polynomial solutions (not necessarily constant but ...
Claudia Valls
doaj +3 more sources
Polynomial Solutions of the Heun Equation
Acta Polytechnica, 2011 We review properties of certain types of polynomial solutions of the Heun equation. Two aspects are particularly concerned, the interlacing property of spectral and Stieltjes polynomials in the case of real roots of these polynomials and asymptotic root ...
B. Shapiro, M. Tater
doaj +4 more sources
A review on applications of holomorphic embedding methods
iEnergy, 2023 The holomorphic embedding method (HEM) stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables.
Kaiyang Huang, Kai Sun
doaj +1 more source
The Polynomial Solutions of Quadratic Diophantine Equation X2−ptY2+2KtX+2ptLtY = 0
Journal of Mathematics, 2021 In this study, we consider the number of polynomial solutions of the Pell equation x2−pty2=2 is formulated for a nonsquare polynomial pt using the polynomial solutions of the Pell equation x2−pty2=1.
Hasan Sankari, Ahmad Abdo
doaj +1 more source
On generalized Heun equation with some mathematical properties
Acta Polytechnica, 2022 We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters.
Nasser Saad
doaj +1 more source
NORMAL BGG SOLUTIONS AND POLYNOMIALS [PDF]
International Journal of Mathematics, 2012 First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries and many other widely studied PDE of geometric origin.
Cap, Andreas +2 more
openaire +5 more sources
Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length [PDF]
Journal of the ACM, 2017 The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class P of languages computable in polynomial time in terms of differential equations with polynomial right-hand side ...
Bournez, Olivier +2 more
openaire +4 more sources
On Polynomial Solutions of Pell’s Equation
Journal of Mathematics, 2021 Polynomial Pell’s equation is x2−Dy2=±1, where D is a quadratic polynomial with integer coefficients and the solutions X,Y must be quadratic polynomials with integer coefficients. Let D=a2x2+a1x+a0 be a polynomial in Zx.
Hasan Sankari, Ahmad Abdo
doaj +1 more source