A multiplicity result for a class of fractional p-Laplacian equations with perturbations in ℝN

2019 ◽  
Vol 65 (7) ◽  
pp. 1219-1255
Author(s):  
Xia Zhang ◽  
Binlin Zhang
Keyword(s):  
Multiplicity Result ◽  
Laplacian Equations

scholarly journals Multiplicity result for non-homogeneous fractional Schrodinger--Kirchhoff-type equations in ℝn

2018 ◽  
Vol 7 (3) ◽  
pp. 247-257 ◽  
Author(s):  
César E. Torres Ledesma
Keyword(s):  
Continuous Function ◽  
Potential Function ◽  
Multiple Solutions ◽  
Laplacian Operator ◽  
Multiplicity Result ◽  
Kirchhoff Type ◽  
Perturbation Term ◽  
New Criterion ◽  
Laplacian Equations

AbstractIn this paper we consider the existence of multiple solutions for the non-homogeneous fractional p-Laplacian equations of Schrödinger–Kirchhoff typeM\Bigg{(}\int_{\mathbb{R}^{n}}\int_{\mathbb{R}^{n}}\frac{|u(x)-u(z)|^{p}}{|x-{% z}|^{n+ps}}\,dz\,dx\Bigg{)}(-\Delta)_{p}^{s}u+V(x)|u|^{p-2}u=f(x,u)+g(x)in {\mathbb{R}^{n}}, where (-Δ)_{p}^{s} is the fractional p-Laplacian operator with 0¡s¡1¡p¡\infty, ps¡n, f : \mathbb{R}^{n}\times\mathbb{R}\to\mathbb{R} is a continuous function, V : \mathbb{R}^{n}\to\mathbb{R}^{+} is a potential function and g : \mathbb{R}^{n}\to\mathbb{R} is a perturbation term. Assuming that the potential V is bounded from bellow, that f(x,t) satisfies the Ambrosetti–Rabinowitz condition and some other reasonable hypotheses, and that g(x) is sufficiently small in L^{p^{\prime}}(\mathbb{R}^{n}), we obtain some new criterion to guarantee that the equation above has at least two non-trivial solutions.

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

scholarly journals A MULTIPLICITY RESULT FOR A CLASS OF EQUATIONS OFp-LAPLACIAN TYPE WITH SIGN-CHANGING NONLINEARITIES

2009 ◽  
Vol 51 (3) ◽  
pp. 513-524 ◽  
Author(s):  
NGUYEN THANH CHUNG ◽  
QUỐC ANH NGÔ
Keyword(s):  
Bounded Domain ◽  
Multiplicity Result ◽  
Positive Parameter ◽  
Existence And Multiplicity ◽  
Carathéodory Function ◽  
Image Position

AbstractUsing variational arguments we study the non-existence and multiplicity of non-negative solutions for a class equations of the formwhere Ω is a bounded domain inN,N≧ 3,fis a sign-changing Carathéodory function on Ω × [0, +∞) and λ is a positive parameter.

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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