Browsing by Author "Wei, Juncheng"
Now showing items 1-20 of 20
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(IOP PUBLISHING LTD, 2006-03)We consider the boundary value problem: Delta u - au + epsilon(2)e(u) = 0, u > 0 in Omega, sigma u/sigma v = 0 on sigma Omega, which is equivalent to the stationary Keller-Segel system from chemotaxis. Here Omega subset ...
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(Elsevier, 2014-01-15)We consider the semilinear equation epsilon(2s)(-Delta)(s)u + V(x)u - u(p) = 0, u > 0, u is an element of H-2s(R-N) where 0 < s < 1, 1 < p < N+2s/N-2s, V (x) is a sufficiently smooth potential with inf(R) V(x) > ...
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(ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2008-12)We consider the Allen-Cahn equation Delta u + u(1 - u(2)) = 0 in R-N. A celebrated conjecture by E. De Giorgi (1978) states that if u is it bounded Solution to this problem Such that partial derivative(xN) u > 0, then ...
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(ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2008-12)We consider the Allen–Cahn equation u +u 1− u2 =0 inRN. A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xNu>0, then the level sets {u=λ}, λ ∈R, ...
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(Springer, 2015)In this paper, we construct a wealth of bounded, entire solutions of the Allen–Cahn equation in the plane. The asymptotic behavior at infinity of these solutions is determined by 2L half affine lines, in the sense that, ...
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(SPRINGER, 2008-08)We consider the elliptic problem Delta u + u(p) = 0, u > 0 in an exterior domain, Omega = R-N\D under zero Dirichlet and vanishing conditions, where D is smooth and bounded in R-N, N >= 3, and p is supercritical, namely p ...
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(Springer, 2015)We consider the standing-wave problem for a nonlinear Schrödinger equation, corresponding to the semilinear elliptic problem − u + V(x)u = |u|p−1u, u ∈ H1(R2), where V(x) is a uniformly positive potential and p > 1. ...
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(2010-11)Let (M, ˜g) be an N-dimensional smooth (compact or noncompact) Riemannian manifold. We introduce the elliptic Jacobi-Toda system on (M, ˜g). We review various recent results on its role in the construction of solutions ...
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(Elsevier, 2014)We consider Liouville-type and partial regularity results for then online arfourth-order problem Δ2u = |u|p−1u in Rn, where p>1 and n≥ 1.We give a complete classification of stableand finite Morse index solutions ...
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(2010)We construct a new class of entire solutions for the Allen-Cahn equation u + (1 u2)u = 0, in R2( C). Given k 1, we nd a family of solutions whose zero level sets are, away from a compact set, asymptotic to 2k ...
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(Elsevier, 2016)We prove sharp Holder continuity and an estimate of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent Delta u =1/u(p) in Omega, p > 1. As a consequence, we prove the ...
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(SIAM PUBLICATIONS, 2006)We consider the problem epsilon(2)Delta u + (u - a(x))(1 - u(2)) = 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega is a smooth and bounded domain in R-2, - 1 < a( x) < 1. ...
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(Duke Univ Press, 2015)For all N >= 9, we find smooth entire epigraphs in R-N, namely, smooth domains of the form Omega := {x is an element of R-N broken vertical bar X-N broken vertical bar > F(X-1, . . . , X-N-1)}, which are not half-spaces ...
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(Taylor & Francis, 2015)The Allen-Cahn equation - Delta u = u - u (3) in DOUBLE-STRUCK CAPITAL R-2 has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem -u '' =u - u (3). In this paper ...
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(SPRINGER, 2006-10)We consider the boundary value problem Du = 0 in Omega, partial derivative u/partial derivative v = 2 lambda sinh u on partial derivative Omega where Omega is a smooth and bounded domain in R-2 and lambda > 0. We prove ...
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(Springer, 2020)We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S-2, u(t) = Delta u + vertical bar del u vertical bar(2)u in Omega x (0, T) u = phi on partial derivative Omega x (0, ...
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(2007)Let V (x) be a non-negative, bounded potential in R-N, N >= 3 and p supercritical, p > N+2/N-2. We look for positive solutions of the standing-wave nonlinear Schrodinger equation Delta u - V(x)u + u(P) = 0 in R-N, with ...
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(2007)Let D be a bounded, smooth domain in R-N, N >= 3, P is an element of D. We consider the boundary value problem in Omega = D \ B delta (P), Delta u +u(p) =0, u > 0 i n Omega, u = 0 on partial derivative Omega, with p ...
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(Springer Berlin, 2008-10)We consider the Allen-Cahn equation "2 u+(1−u2)u = 0 in a bounded, smooth domain in R2, under zero Neumann boundary conditions, where " > 0 is a small parameter. Let 0 be a segment contained in , connecting ...
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(2010)We construct a new class of positive solutions for the classical elliptic problem ¢u ¡ u + up = 0; p > 2; in R2: We establish a deep relation between them and the following Toda system c2f00 j = efj¡1¡fj ¡ efj¡fj+1 in ...
