scholarly journals Existence and multiplicity of solutions for ap(x)-Laplacian equation with critical growth

2013 ◽  
Vol 403 (1) ◽  
pp. 143-154 ◽  
Author(s):  
Claudianor O. Alves ◽  
José L.P. Barreiro
Keyword(s):  
Critical Growth ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

scholarly journals Existence and multiplicity of solutions for a Kirchhoff system with critical growth

2021 ◽  
Vol 46 (1) ◽  
pp. 295-308
Author(s):  
Marcelo F. Furtado ◽  
Luan D. de Oliveira ◽  
João Pablo P. da Silva
Keyword(s):  
Critical Growth ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals On Dirichlet problem for fractional p-Laplacian with singular non-linearity

2016 ◽  
Vol 8 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega} , {n>sp} , {s\in(0,1)} , {\lambda>0} , {0<q\leq 1} and {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.

scholarly journals Existence and multiplicity of solutions for fractional Schödinger equation involving a critical nonlinearity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongzhen Yun ◽  
Tianqing An ◽  
Guoju Ye
Keyword(s):  
Variational Method ◽  
Existence Results ◽  
Critical Growth ◽  
Concentration Compactness ◽  
Critical Nonlinearity ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

AbstractIn this paper, we investigate the fractional Schödinger equation involving a critical growth. By using the principle of concentration compactness and the variational method, we obtain some new existence results for the above equation, which improve the related results on this topic.

Multiple solutions for the p-Laplacian equations with concave nonlinearities via Morse theory

2017 ◽  
Vol 19 (03) ◽  
pp. 1650014 ◽  
Author(s):  
Mingzheng Sun ◽  
Jiabao Su ◽  
Hongrui Cai
Keyword(s):  
Growth Condition ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Subcritical Growth ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Global Condition ◽  
Laplacian Equations

In this paper, by Morse theory, we study the existence and multiplicity of solutions for the [Formula: see text]-Laplacian equation with a “concave” nonlinearity and a parameter. In our results, we do not need any additional global condition on the nonlinearities, except for a subcritical growth condition.

The Nehari manifold approach for N-Laplace equation with singular and exponential nonlinearities in ℝN

2015 ◽  
Vol 17 (03) ◽  
pp. 1450011 ◽  
Author(s):  
Sarika Goyal ◽  
K. Sreenadh
Keyword(s):  
Positive Solutions ◽  
Laplace Equation ◽  
Nehari Manifold ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this article, we study the existence and multiplicity of solutions of the singular N-Laplacian equation: [Formula: see text] where N ≥ 2, 0 ≤ q < N - 1 < p + 1, β ∈ [0, N), λ > 0, and h ≥ 0 in ℝN. Using the nature of the Nehari manifold and fibering maps associated with the Euler functional, we prove that there exists λ0such that for λ ∈ (0, λ0), the problem admits at least two positive solutions. We also show that when h(x) > 0, there exists λ0such that (Pλ) has no solution for λ > λ0.

Sign in / Sign up

Export Citation Format

Share Document