scholarly journals Existence And Multiplicity Of Solutions For A Robin Problem

2014 ◽  
Vol 10 (03) ◽  
pp. 163-172
Author(s):  
Mostafa Allaoui ◽  
Abdel Rachid El Amrouss ◽  
Fouad Kissi ◽  
Anass Ourraoui
Keyword(s):  
Robin Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals On a Robin type problem involving 𝑝(𝑥)-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdesslem Ayoujil ◽  
Anass Ourraoui
Keyword(s):  
Variational Approach ◽  
Growth Conditions ◽  
Laplacian Operator ◽  
Robin Problem ◽  
Type Problem ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Cerami Condition ◽  
Weaker Conditions

Abstract This paper deals with the existence and multiplicity of solutions for the p ⁢ ( x ) p(x) -Laplacian Robin problem without the well-known Ambrosetti–Rabinowitz type growth conditions. By means of the variational approach (with the Cerami condition), existence and multiplicity results of solutions are established under weaker conditions.

scholarly journals Existence of Solutions for a Robin Problem Involving thep(x)-Laplace Operator

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Mostafa Allaoui
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Laplace Operator ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Robin Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

In this article we study the nonlinear Robin boundary-value problem-Δp(x)u=f(x,u)  in  Ω,|∇u|px-2(∂u/∂ν)+β(x)up(x)-2u=0on∂Ω. Using the variational method, under appropriate assumptions onf, we obtain results on existence and multiplicity of solutions.

scholarly journals Multiplicity of solutions for Robin problem involving the p(x)-laplacian

2021 ◽  
Vol 13 (2) ◽  
pp. 321-335
Author(s):  
Hassan Belaouidel ◽  
Anass Ourraoui ◽  
Najib Tsouli
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Robin Boundary Condition ◽  
Robin Problem ◽  
Technical Approach ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Laplacian Equations

Abstract This paper is concerned with the existence and multiplicity of solutions for p(x)-Laplacian equations with Robin boundary condition. Our technical approach is based on variational methods.

scholarly journals Existence and Multiplicity of Solutions for a Robin Problem Involving the p(x)-Laplace Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Najib Tsouli ◽  
Omar Chakrone ◽  
Omar Darhouche ◽  
Mostafa Rahmani
Keyword(s):  
Continuous Function ◽  
Variational Method ◽  
Smooth Boundary ◽  
Normal Derivative ◽  
Robin Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Robin Boundary Value Problem ◽  
Outer Unit

We study the following nonlinear Robin boundary-value problem −Δp(x)u=λf(x,u) in Ω, |∇u|p(x)-2(∂u/∂v)+β(x)|u|p(x)−2u=0 on ∂Ω, where Ω⊂ℝN is a bounded domain with smooth boundary ∂Ω, ∂u/∂v is the outer unit normal derivative on ∂Ω, λ>0 is a real number, p is a continuous function on Ω¯ with infx∈Ω¯p(x)>1, β∈L∞(∂Ω) with β−:=infx∈∂Ωβ(x)>0, and f:Ω×ℝ→ℝ is a continuous function. Using the variational method, under appropriate assumptions on f, we obtain results on existence and multiplicity of solutions.

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.

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