scholarly journals Regularity of the extremal solution for some elliptic problems with singular nonlinearity and advection

2011 ◽  
Vol 251 (8) ◽  
pp. 2082-2099 ◽  
Author(s):  
Xue Luo ◽  
Dong Ye ◽  
Feng Zhou
Keyword(s):  
Elliptic Problems ◽  
Extremal Solution ◽  
Singular Nonlinearity

scholarly journals Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Baishun Lai
Keyword(s):  
Weak Solution ◽  
Unique Solution ◽  
Biharmonic Equation ◽  
Final Section ◽  
Elliptic Problems ◽  
Weak Sense ◽  
Extremal Case ◽  
Singular Nonlinearity

We study the following semilinear biharmonic equation  , which satisfies0<u̲λ<1. In the extremal caseλ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. Besides, several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section.

scholarly journals Bifurcations of some elliptic problems with a singular nonlinearity via Morse index

2010 ◽  
Vol 10 (2) ◽  
pp. 507-525 ◽  
Author(s):  
Zongming Guo ◽  
Zhongyuan Liu ◽  
Juncheng Wei ◽  
Feng Zhou
Keyword(s):  
Morse Index ◽  
Elliptic Problems ◽  
Singular Nonlinearity
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