scholarly journals Polyharmonic equations with critical exponential growth in the whole space $ \mathbb{R}^{n}$

2015 ◽  
Vol 36 (2) ◽  
pp. 577-600 ◽  
Author(s):  
Guozhen Lu ◽  
Nguyen Lam ◽  
Jiguang Bao
Keyword(s):  
Exponential Growth ◽  
Polyharmonic Equations ◽  
Whole Space ◽  
Critical Exponential Growth

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.

Existence of nontrivial solutions to quasilinear polyharmonic equations with critical exponential growth

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarika Goyal ◽  
Konijeti Sreenadh
Keyword(s):  
Nontrivial Solution ◽  
Exponential Growth ◽  
Nontrivial Solutions ◽  
Polyharmonic Equation ◽  
Polyharmonic Equations ◽  
Critical Exponential Growth

AbstractIn this article, we show the existence of a nontrivial solution of the quasilinear polyharmonic equation Δ

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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