scholarly journals Publisher’s Note: “Existence and multiplicity of solutions for the fractional p-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth” [J. Math. Phys. 62, 051507 (2021)]

2021 ◽  
Vol 62 (6) ◽  
pp. 069901
Author(s):  
Eduardo de S. Böer ◽  
Olímpio H. Miyagaki
Keyword(s):  
Subcritical Growth ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Logarithmic Equation ◽  
Math Phys

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.

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.

Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝN

2018 ◽  
Vol 24 (3) ◽  
pp. 1231-1248
Author(s):  
Claudianor O. Alves ◽  
Alan C.B. dos Santos
Keyword(s):  
Field Equation ◽  
Continuous Function ◽  
Singular Function ◽  
Positive Continuous Function ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic

In this paper, we establish existence and multiplicity of solutions for the following class of quasilinear field equation    −Δu + V(x)u − Δpu + W′(u) = 0,  in  ℝN,    (P) where u = (u1, u2, … , uN+1), p > N ≥ 2, W is a singular function and V is a positive continuous function.

scholarly journals Solutions of Nonlocal -Laplacian Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mustafa Avci ◽  
Rabil Ayazoglu (Mashiyev)
Keyword(s):  
Laplace Operator ◽  
Variational Approach ◽  
Nonlocal Problem ◽  
Type Equation ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Equation ◽  
Laplacian Equations

In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

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