Existence and multiplicity of solutions for a class ofp&qelliptic problems with critical exponent

2013 ◽  
Vol 286 (11-12) ◽  
pp. 1129-1141 ◽  
Author(s):  
Giovany M. Figueiredo
Keyword(s):  
Critical Exponent ◽  
Multiplicity Of Solutions ◽  
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 Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

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.

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