scholarly journals A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface

2007 ◽  
Vol 359 (12) ◽  
pp. 5761-5777 ◽  
Author(s):  
Yunyan Yang
Keyword(s):  
Riemannian Surface ◽  
Sharp Form ◽  
Trudinger Inequality

Expansive geodesic flows on surfaces

1993 ◽  
Vol 13 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Miguel Paternain
Keyword(s):  
Geodesic Flow ◽  
Compact Surface ◽  
Conjugate Points ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Flows On Surfaces

AbstractWe prove the following result: if M is a compact Riemannian surface whose geodesic flow is expansive, then M has no conjugate points. This result and the techniques of E. Ghys imply that all expansive geodesic flows of a compact surface are topologically equivalent.

N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Nguyen Lam ◽  
Guozhen Lu
Keyword(s):  
Bounded Domain ◽  
Exponential Growth ◽  
Nonnegative Solution ◽  
Nontrivial Solutions ◽  
Critical Exponential Growth ◽  
Trudinger Inequality ◽  
Laplacian Equations

AbstractLet Ω be a bounded domain in ℝwhen f is of subcritical or critical exponential growth. This nonlinearity is motivated by the Moser-Trudinger inequality. In fact, we will prove the existence of a nontrivial nonnegative solution to (0.1) without the Ambrosetti-Rabinowitz (AR) condition. Earlier works in the literature on the existence of nontrivial solutions to N−Laplacian in ℝ

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