The existence of a nontrivial solution to p-Laplacian equations in RN with supercritical growth

2012 ◽  
Vol 36 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Gongbao Li ◽  
Chunhua Wang
Keyword(s):  
Nontrivial Solution ◽  
Laplacian Equations

scholarly journals Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Huxiao Luo ◽  
Shengjun Li ◽  
Xianhua Tang
Keyword(s):  
Weak Solution ◽  
Nontrivial Solution ◽  
Perturbation Methods ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Weak Limit ◽  
Main Difficulty ◽  
Potential Term ◽  
Laplacian Equation ◽  
Laplacian Equations

We study the existence of nontrivial solution of the following equation without compactness: (-Δ)pαu+up-2u=f(x,u),  x∈RN, where N,p≥2,  α∈(0,1),  (-Δ)pα is the fractional p-Laplacian, and the subcritical p-superlinear term f∈C(RN×R) is 1-periodic in xi for i=1,2,…,N. Our main difficulty is that the weak limit of (PS) sequence is not always the weak solution of fractional p-Laplacian type equation. To overcome this difficulty, by adding coercive potential term and using mountain pass theorem, we get the weak solution uλ of perturbation equations. And we prove that uλ→u as λ→0. Finally, by using vanishing lemma and periodic condition, we get that u is a nontrivial solution of fractional p-Laplacian equation.

Uniform attractors for non-autonomous -Laplacian equations

2008 ◽  
Vol 68 (11) ◽  
pp. 3349-3363 ◽  
Author(s):  
Guang-xia Chen ◽  
Cheng-Kui Zhong
Keyword(s):  
Uniform Attractors ◽  
Laplacian Equations

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 of infinitely many solutions for fractional p-Laplacian Schrödinger–Kirchhof-Type equations with general potentials

2021 ◽  
pp. 2250095
Author(s):  
Ghania Benhamida ◽  
Toufik Moussaoui
Keyword(s):  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Kirchhoff Type ◽  
Laplacian Equations

In this paper, we use the genus properties in critical point theory to prove the existence of infinitely many solutions for fractional [Formula: see text]-Laplacian equations of Schrödinger-Kirchhoff type.

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