Non Linear Parabolic Evolutions in Unbounded Domains

1994 ◽  
pp. 97-104 ◽  
Author(s):  
P. Collet
Keyword(s):  
Unbounded Domains ◽  
Non Linear

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

Minimum action solutions of non-linear elliptic equations in unbounded domains containing a plane

1986 ◽  
Vol 102 (3-4) ◽  
pp. 327-343 ◽  
Author(s):  
Otared Kavian
Keyword(s):  
Elliptic Equation ◽  
Continuous Function ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Unbounded Domains ◽  
Necessary And Sufficient Conditions ◽  
Smooth Bounded Domain ◽  
Non Linear ◽  
Necessary And Sufficient

SynopsisLet d ≧ 1 be an integer and ω ⊂ℝd a smooth bounded domain and consider the elliptic equation − Δu = g(u) on Ω = ℝ2 × ω. We prove that under (almost) necessary and sufficient conditions on the continuous function g: ℝm→ ℝm the above equation has a minimum-action solution.

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