Classical solutions for some higher order semilinear elliptic equations under weak growth conditions

1997 ◽  
Vol 28 (5) ◽  
pp. 799-807 ◽  
Author(s):  
Hans-Christoph Grunau ◽  
Guido Sweers
Keyword(s):  
Elliptic Equations ◽  
Growth Conditions ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Classical Solutions ◽  
Semilinear Elliptic ◽  
Weak Growth

Semilinear elliptic and parabolic equations of arbitrary order

1978 ◽  
Vol 78 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Wolf von Wahl ◽  
J. B. McLeod
Keyword(s):  
Parabolic Equations ◽  
Elliptic Equations ◽  
Principal Part ◽  
Arbitrary Order ◽  
Growth Conditions ◽  
Semilinear Elliptic Equations ◽  
Classical Solutions ◽  
Semilinear Elliptic ◽  
Elliptic And Parabolic Equations

In this paper we prove the existence of classical solutions for all t ≧ 0 for parabolic equations u′ + A(t)u = –f(u, ∇y, …, ∇2m–2u) of arbitrary order. 2m is the order of the elliptic principal part. f must satisfy some monotonicity and growth conditions. Moreover, similar results are also valid for semilinear elliptic equations.

scholarly journals MAXIMUM PRINCIPLES FOR SOME HIGHER-ORDER SEMILINEAR ELLIPTIC EQUATIONS

2010 ◽  
Vol 53 (2) ◽  
pp. 313-320 ◽  
Author(s):  
A. MARENO
Keyword(s):  
Elliptic Equations ◽  
Auxiliary Function ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Maximum Principles ◽  
Eighth Order ◽  
Analyse Math ◽  
Semilinear Elliptic

AbstractWe deduce maximum principles for fourth-, sixth- and eighth-order elliptic equations by modifying an auxiliary function introduced by Payne (J. Analyse Math. 30 (1976), 421–433). Integral bounds on various gradients of the solutions of these equations are obtained.

scholarly journals Microscopic asymptotics for solutions of some semilinear Elliptic equations

1995 ◽  
Vol 138 ◽  
pp. 33-50
Author(s):  
Takayoshi Ogawa ◽  
Takashi Suzuki
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Classical Solutions ◽  
Semilinear Elliptic ◽  
The Family

In our previous work [8], we picked up the elliptic equation(1) with the nonlinearity f(u) ⊇ 0 in C1. We studied the asymptotics of the family {(λ, u(x))} of classical solutions satisfying(2)

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