Multiple solvability of certain elliptic problems with critical nonlinearity exponents

1992 ◽  
Vol 52 (1) ◽  
pp. 668-672
Author(s):  
I. A. Kuzin
Keyword(s):  
Elliptic Problems ◽  
Critical Nonlinearity

scholarly journals Multiple solutions of Neumann elliptic problems with critical nonlinearity

1999 ◽  
Vol 5 (2) ◽  
pp. 301-320
Author(s):  
Monica Musso ◽  
◽  
Donato Passaseo
Keyword(s):  
Multiple Solutions ◽  
Elliptic Problems ◽  
Critical Nonlinearity

scholarly journals Positive solutions for elliptic problems with critical nonlinearity and combined singularity

2010 ◽  
Vol 135 (4) ◽  
pp. 413-422 ◽  
Author(s):  
Jianqing Chen ◽  
Eugénio M. Rocha
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Critical Nonlinearity

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

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