Results 231 to 240 of about 625,582 (261)

On p Laplace polynomial solutions

The Journal of Analysis, 2016
This paper investigates the existence of real homogeneous polynomial solutions of the \(p\)-Laplace equation \(\mathrm{div}(\left| \nabla u\right| ^{p-2}\nabla u)=0\) on \(\mathbb{R}^{n}\) (\(n\geq 3\)), where \(p\in \mathbb{R}\backslash \{1,2\}\). Recently, Tkachev showed that there are no such solutions of degree \(3\).
Lewis, John L., Vogel, Andrew
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Simultaneous solution of polynomial equations

Applied Mathematics and Computation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Celik, E, Bayram, M
openaire   +3 more sources

Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

Qualitative Theory of Dynamical Systems, 2017
A traveling wave solution \(u= U(x-ct)\) of a partial differential equation \(u_{xx}= F(u,u_x,u_t)\) is called an algebraic traveling wave solution if there exists a polynomial \(p\) such that \(p(U,U')= 0\). The author completely characterizes the existence of algebraic traveling wave solutions of the partial differential equation \[ u_t= du_{xx}- a(u-
openaire   +2 more sources

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