Ground states for planar Hamiltonian elliptic systems with critical exponential growth

2022 ◽  
Vol 308 ◽  
pp. 130-159
Author(s):  
Dongdong Qin ◽  
Xianhua Tang ◽  
Jian Zhang
Keyword(s):  
Exponential Growth ◽  
Ground States ◽  
Elliptic Systems ◽  
Critical Exponential Growth

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

2018 ◽  
Vol 292 (1) ◽  
pp. 137-158
Author(s):  
Sergio H. Monari Soares ◽  
Yony R. Santaria Leuyacc
Keyword(s):  
Exponential Growth ◽  
Elliptic Systems ◽  
Critical Exponential Growth

scholarly journals Ground state solutions for a Kirchhoff type elliptic systems involving critical exponential growth nonlinearities

2021 ◽  
Author(s):  
Shengbing Deng ◽  
Tingting Huang
Keyword(s):  
Ground State ◽  
Exponential Growth ◽  
Elliptic Systems ◽  
Ground State Solution ◽  
State Solution ◽  
Ground State Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Growth Nonlinearities

The aim of this paper is to study the ground state solution for a Kirchhoff type elliptic systems without the Ambrosetti-Rabinowitz condition.

scholarly journals (p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

2020 ◽  
Vol 18 (1) ◽  
pp. 1423-1439
Author(s):  
Patrizia Pucci ◽  
Letizia Temperini
Keyword(s):  
Heisenberg Group ◽  
Exponential Growth ◽  
Existence Of Solutions ◽  
Elliptic Systems ◽  
Singular Behavior ◽  
Actual System ◽  
Exponential Term ◽  
Nonnegative Solutions ◽  
Critical Exponential Growth

Abstract The paper deals with the existence of solutions for (p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set in {{\mathbb{H}}}^{n} .

Adams Type Inequality and Application for a Class of Polyharmonic Equations with Critical Growth

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
João Marcos do Ó ◽  
Abiel Costa Macedo
Keyword(s):  
Sobolev Space ◽  
Exponential Growth ◽  
Type Inequality ◽  
Critical Growth ◽  
Polyharmonic Equations ◽  
Critical Exponential Growth

AbstractIn this paper we give a new Adams type inequality for the Sobolev space W(−Δ)where the nonlinearity is “superlinear” and has critical exponential growth at infinite.

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