scholarly journals Lusternik-Schnirelman category and nonlinear elliptic eigenvalue problems

1965 ◽  
Vol 71 (4) ◽  
pp. 644-649 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Eigenvalue Problems ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems

scholarly journals Two-grid methods for a class of nonlinear elliptic eigenvalue problems

2017 ◽  
Vol 38 (2) ◽  
pp. 605-645 ◽  
Author(s):  
Eric Cancès ◽  
Rachida Chakir ◽  
Lianhua He ◽  
Yvon Maday
Keyword(s):  
Eigenvalue Problems ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems

A MULTIGRID-LANCZOS ALGORITHM FOR THE NUMERICAL SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS

2003 ◽  
Vol 13 (05) ◽  
pp. 1217-1228 ◽  
Author(s):  
S.-L. CHANG ◽  
C.-S. CHIEN
Keyword(s):  
Numerical Methods ◽  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Lanczos Method ◽  
Convergence Theory ◽  
Lanczos Algorithm ◽  
Nonlinear Eigenvalue Problems ◽  
Nonlinear Elliptic ◽  
Discrete Problems ◽  
Elliptic Eigenvalue Problems

We study numerical methods for solving nonlinear elliptic eigenvalue problems which contain folds and bifurcation points. First we present some convergence theory for the MINRES, a variant of the Lanczos method. A multigrid-Lanczos method is then proposed for tracking solution branches of associated discrete problems and detecting singular points along solution branches. The proposed algorithm has the advantage of being robust and can be easily implemented. It can be regarded as a generalization and an improvement of the continuation-Lanczos algorithm. Our numerical results show the efficiency of this algorithm.

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