Asymptotics of solutions of some nonlinear elliptic systems

Journal Article · Mon Dec 30 23:00:00 EST 1996 · Communications in Partial Differential Equations

OSTI ID:437563

Bidaut-Veron, M F; Raoux, T ^[1]

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1. Faculte des Sciences, Tours (France)

This paper deals with the local and global behaviour of the positive solutions of the semilinear elliptic system in R{sup N} (N{ge}3) {Delta}u+{vert_bar}x{vert_bar}{sup {sigma}}u{sup q}v{sup p+1} =0, {Delta}v+{vert_bar}x{vert_bar}{sup {sigma}}u{sup q+1}v{sup p}=0, where {sigma},p,q{epsilon}R, and p,q>0. Our main results in the fact that the solutions satisfy Harnack inequality when Q = p+q+1<(N+2)/(N-2), which gives local estimates. Without this assumption on Q, we give the precise behaviour of the solutions, provided that these estimates are true. When Q < (N+2)/(N-2), the solutions can also present an anisotropic behaviour. 34 refs.

• OSTI ID: 437563
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 7-8 Vol. 21; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ASYMPTOTIC SOLUTIONS
CONVERGENCE
ELLIPTICAL CONFIGURATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS