scholarly journals Verified computations to semilinear elliptic boundary value problems on arbitrary polygonal domains

2013 ◽  
Vol 4 (1) ◽  
pp. 34-61 ◽  
Author(s):  
Akitoshi Takayasu ◽  
Xuefeng Liu ◽  
Shin'ichi Oishi
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Polygonal Domains ◽  
Semilinear Elliptic ◽  
Verified Computations

Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist

2001 ◽  
Vol 131 (3) ◽  
pp. 721-732 ◽  
Author(s):  
Shujie Li ◽  
Kanishka Perera ◽  
Jiabao Su
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Elliptic Boundary Value Problems ◽  
Critical Groups ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic

We compute critical groups in semilinear elliptic boundary-value problems in which the nonlinear term may fail to have asymptotic limits at zero and at infinity. As applications, we prove several new existence results.

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