scholarly journals Elliptic equations with discontinuous nonlinearities\\ of exponential growth

2021 ◽  
Author(s):  
Вячеслав Павленко ◽  
Дмитрий Потапов
Keyword(s):  
Exponential Growth ◽  
Elliptic Equations ◽  
Discontinuous Nonlinearities

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

ELLIPTIC EQUATIONS IN ℝ2 WITH ONE-SIDED EXPONENTIAL GROWTH

2004 ◽  
Vol 06 (06) ◽  
pp. 947-971 ◽  
Author(s):  
ZHITAO ZHANG ◽  
MARTA CALANCHI ◽  
BERNHARD RUF
Keyword(s):  
Exponential Growth ◽  
Elliptic Equations ◽  
Morse Index ◽  
Linear Growth ◽  
Critical Growth ◽  
The Other ◽  
Critical Groups ◽  
Bounded Domains ◽  
Eigen Value

We consider elliptic equations in bounded domains Ω⊂ℝ2 with nonlinearities which have exponential growth at +∞ (subcritical and critical growth, respectively) and linear growth λ at -∞, with λ>λ1, the first eigen value of the Laplacian. We prove that such equations have at least two solutions for certain forcing terms; one solution is negative, the other one is sign-changing. Some critical groups and Morse index of these solutions are given. Also the case λ<λ1 is considered.

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