scholarly journals Mountain pass theorem in ordered Banach spaces and its applications to semilinear elliptic equations

2011 ◽  
Vol 19 (2) ◽  
pp. 159-175 ◽  
Author(s):  
Ryuji Kajikiya
Keyword(s):  
Banach Spaces ◽  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Equations ◽  
Mountain Pass ◽  
Semilinear Elliptic ◽  
Ordered Banach Spaces

Semilinear elliptic equations of the Hénon-type in hyperbolic space

2016 ◽  
Vol 18 (02) ◽  
pp. 1550026 ◽  
Author(s):  
P. C. Carrião ◽  
L. F. O. Faria ◽  
O. H. Miyagaki
Keyword(s):  
Unit Ball ◽  
Positive Solution ◽  
Hyperbolic Space ◽  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Equations ◽  
Mountain Pass ◽  
Sobolev Embedding ◽  
Radial Functions ◽  
Semilinear Elliptic

This paper deals with a class of the semilinear elliptic equations of the Hénon-type in hyperbolic space. The problem involves a logarithm weight in the Poincaré ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former Ni result made for a unit ball in [Formula: see text] Combining this compactness embedding with the Mountain Pass Theorem, a result of the existence of positive solution is established.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

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