ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASI LINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS

1987 ◽  
Vol 7 (4) ◽  
pp. 447-459 ◽  
Author(s):  
Jianfu Yang ◽  
Xiping Zhu
Keyword(s):  
Boundary Value Problem ◽  
Nontrivial Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Linear Elliptic Boundary

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.

scholarly journals On an asymptotically linear elliptic Dirichlet problem

2002 ◽  
Vol 7 (10) ◽  
pp. 509-516 ◽  
Author(s):  
Zhitao Zhang ◽  
Shujie Li ◽  
Shibo Liu ◽  
Weijie Feng
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Negative Solution ◽  
Asymptotically Linear ◽  
Elliptic Boundary Value ◽  
Resonant Case ◽  
Linear Elliptic Boundary

Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS) sequence of the corresponding functional. Moreover, the proof is very simple.

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