scholarly journals Existence of nontrivial solutions to Polyharmonic equations with subcritical and critical exponential growth

2012 ◽  
Vol 32 (6) ◽  
pp. 2187-2205 ◽  
Author(s):  
Nguyen Lam ◽  
◽  
Guozhen Lu
Keyword(s):  
Exponential Growth ◽  
Nontrivial Solutions ◽  
Polyharmonic Equations ◽  
Critical Exponential Growth

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

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.

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

Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Patrizia Pucci ◽  
Letizia Temperini
Keyword(s):  
Heisenberg Group ◽  
Elliptic Operator ◽  
Exponential Growth ◽  
Singular Behavior ◽  
Nontrivial Solutions ◽  
Right Hand ◽  
Critical Exponential Growth ◽  
The Right

Abstract The paper deals with the existence of nontrivial solutions for ( p , Q ) (p,Q) equations in the Heisenberg group H n \mathbb{H}^{n} with critical exponential growth at infinity and a singular behavior at the origin. The main features and novelty of the paper are the above generality on the right-hand side of the equation, the ( p , Q ) (p,Q) growth of the elliptic operator and the fact that the equation is studied in the entire Heisenberg group.

Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ruichang Pei
Keyword(s):  
Exponential Growth ◽  
Polynomial Growth ◽  
Mountain Pass Theorem ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Trudinger Inequality ◽  
Fractional Kirchhoff Type Problems ◽  
Kirchhoff Type Problems ◽  
Subcritical Polynomial Growth

Abstract The main aim of this paper is to investigate the existence of nontrivial solutions for a class of fractional Kirchhoff-type problems with right-hand side nonlinearity which is subcritical or critical exponential growth (subcritical polynomial growth) at infinity. However, it need not satisfy the Ambrosetti–Rabinowitz (AR) condition. Some existence results of nontrivial solutions are established via Mountain Pass Theorem combined with the fractional Moser–Trudinger inequality.

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