Results 11 to 20 of about 3,381,515 (303)
Entire solutions of the euler—poisson equations [PDF]
Ukrainian Mathematical Journal, 2004 Summary: The author gives all entire solutions of the Euler-Poisson equations describing the motion of a rigid body under the action of its own weight.
A. V. Belyaev
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Entire invariant solutions to Monge-Ampère equations [PDF]
Proceedings of the American Mathematical Society, 2004 We prove existence and regularity of entire solutions to Monge-Ampère equations invariant under an irreducible action of a compact Lie group.
Roger Bielawski
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Entire solutions of Donaldson’s equation [PDF]
Pacific Journal of Mathematics, 2012 A serious blunder was found in a previous version of the ...
Weiyong He
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On bounded entire solutions of semilinear elliptic equations [PDF]
Hiroshima Mathematical Journal, 1984 The author gives a result on the existence of infinitely many bounded entire solutions of the nonlinear problems \(-\Delta u+g(x)u^{\gamma}=0,\) \(-\Delta u+g(x)e^ u=0.\) Conditions assuring positivity are also given.
Nichiro Kawano
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Nonexistence of radial entire solutions of elliptic systems [PDF]
Journal of Differential Equations, 2003 The author considers the quasi-variational ordinary differential system \[ [\nabla G(u,u')]'- \nabla_u G(u,u')+ Q(t, u,u')= f(t,u) \] on \(J= (T,\infty)\), \(T\geq 0\), where \(\nabla= \nabla_u\) denotes the gradient operator with respect to the second variable of the function \(G\).
Roberta Filippucci
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Entire positive solution to the system of nonlinear elliptic equations [PDF]
Boundary Value Problems, 2006 The second-order nonlinear elliptic system −Δu=f1(x)uα+g1(x)u−β+h1(x)uγP(v), −Δv=f2(x)vα+g2(x)v−β+h2(x)vγP(u) with ...
Miaoxin Yao, Lingyun Qiu
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Large energy entire solutions for the Yamabe equation
Journal of Differential Equations, 2011 AbstractWe consider the Yamabe equation Δu+n(n−2)4|u|4n−2u=0 in Rn, n⩾3. Let k⩾1 and ξjk=(e2jπik,0)∈Rn=C×Rn−2. For all large k we find a solution of the form uk(x)=U(x)−∑j=1kμk−n−22U×(μk−1(x−ξj))+o(1), where U(x)=(21+|x|2)n−22, μk=cnk2 for n⩾4, μk=ck2(logk)2 for n=3 and o(1)→0 uniformly as k→+∞.
Frank Pacard +4 more
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SOME ENTIRE SOLUTIONS OF THE ALLEN–CAHN EQUATION [PDF]
Taiwanese Journal of Mathematics, 2004 The paper deals with entire solutions of a bistable reaction-diffusion equation with Nagumo type nonlinearity, the so called Allen-Cahn equation. The entire solutions are the solutions defined for all \((x,t)\in (\mathbb{R}\times \mathbb{R}).\) The authors show the existence of an entire solution which behaves as two traveling front solutions coming ...
Fukao, Yukitaka +2 more
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A remark on entire solutions of quasilinear elliptic equations
Journal of Differential Equations, 2011 AbstractBy applying a main comparison theorem of Pucci and Serrin (2007) [2] we cover, for general equations of p-Laplace type, the open cases of Theorems B, D, E of Farina and Serrin (submitted for publication) [1] as described in Problems 2 and 3 of Section 12 of Farina and Serrin (submitted for publication) [1].
PUCCI, Patrizia, J. SERRIN
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Entire solutions of certain type of differential equations II
Journal of Mathematical Analysis and Applications, 2008 AbstractWe analyze the transcendental entire solutions of the following type of nonlinear differential equations: fn(z)+P(f)=p1eα1z+p2eα2z in the complex plane, where p1, p2 and α1, α2 are nonzero constants, and P(f) denotes a differential polynomial in f of degree at most n−1 with small functions of f as the coefficients.
Ping Li
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