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On p Laplace polynomial solutions
The Journal of Analysis, 2016This 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 \(3\).
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Qualitative Theory of Dynamical Systems, 2017A 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-
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