Existence and multiplicity of solutions for p(x)-Laplacian equation with nonsmooth potential

2010 ◽  
Vol 11 (1) ◽  
pp. 106-116 ◽  
Author(s):  
Chenyin Qian ◽  
Zifei Shen
Keyword(s):  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Nonsmooth Potential

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.

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.

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