Elliptic equations with discontinuous nonlinearities in N

1998 ◽  
Vol 31 (1-2) ◽  
pp. 217-227 ◽  
Author(s):  
S. Carl ◽  
S. Heikkilä
Keyword(s):  
Elliptic Equations ◽  
Discontinuous Nonlinearities

scholarly journals Elliptic problems in ℝN with discontinuous nonlinearities

2000 ◽  
Vol 43 (3) ◽  
pp. 545-558
Author(s):  
Gabriele Bonanno ◽  
Salvatore A. Marano
Keyword(s):  
Fixed Points ◽  
Lebesgue Measure ◽  
Elliptic Equations ◽  
Measure Zero ◽  
Elliptic Problems ◽  
Strong Solutions ◽  
Lebesgue Measure Zero ◽  
Zero Set ◽  
Entire Space ◽  
Discontinuous Nonlinearities

AbstractFor a class of elliptic equations in the entire space and with nonlinear terms having a possibly uncountable (but of Lebesgue measure zero) set of discontinuities, the existence of strong solutions is established. Two simple applications are then developed. The approach taken is strictly based on set-valued analysis and fixed-points arguments.

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