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 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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