Are solutions of almost radial nonlinear elliptic equations almost radial?

Journal Article · Sat Dec 30 23:00:00 EST 1995 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309508821162· OSTI ID:482479

Taliaferro, S D ^[1]

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1. Texas A&M Univ., College Station, TX (United States)

In this paper we study the radial properties and asymptotic behavior of solutions of the problem {Delta}u = f(x,u) lim u(x) = {infinity} {vert_bar}x{vert_bar} {yields} {infinity} where f(x,u) is continuous and positive for u > 0 and x {element_of} {Omega} = R{sup n} - {Beta}. Here {Beta} is an open ball with center at the origin and n {ge} 3. We also assume for some {gamma} > 1 that f(x,u)/u{sup {gamma}} {yields} {infinity} as u {yields} {infinity} pointwise in x for {vert_bar}x{vert_bar} sufficiently large. We do not require solutions of (1.1a,b) to be defined for all x in {Omega}, but rather only for {vert_bar}x{vert_bar} sufficiently large. 20 refs.

• Sponsoring Organization: USDOE
• OSTI ID: 482479
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 11-12 Vol. 20; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

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