Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moloud Makvand Chaharlang ◽  
Abdolrahman Razani
Keyword(s):  
Boundary Condition ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Neumann Boundary Condition ◽  
Mountain Pass Theorem ◽  
Minimum Principle ◽  
Neumann Boundary ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

AbstractIn this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces.

Infinitely many solutions for nonlocal elliptic systems in Orlicz–Sobolev spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Samira Heidari ◽  
Abdolrahman Razani
Keyword(s):  
Sobolev Spaces ◽  
Weak Solutions ◽  
Neumann Boundary ◽  
Elliptic Systems ◽  
Type Systems ◽  
Dirichlet Boundary Conditions ◽  
Infinitely Many Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

Abstract Recently, the existence of at least two weak solutions for a Kirchhoff–type problem has been studied in [M. Makvand Chaharlang and A. Razani, Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition, Georgian Math. J. 28 2021, 3, 429–438]. Here, the existence of infinitely many solutions for nonlocal Kirchhoff-type systems including Dirichlet boundary conditions in Orlicz–Sobolev spaces is studied by using variational methods and critical point theory.

scholarly journals ON AN ELLIPTIC SYSTEM OF P(X)-KIRCHHOFF-TYPE UNDER NEUMANN BOUNDARY CONDITION

2012 ◽  
Vol 17 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Zehra Yucedag ◽  
Mustafa Avci ◽  
Rabil Mashiyev
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Principle ◽  
Variational Method ◽  
Elliptic System ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Kirchhoff Type ◽  
Direct Variational Method

In the present paper, by using the direct variational method and the Ekeland variational principle, we study the existence of solutions for an elliptic system of p(x)-Kirchhoff-type under Neumann boundary condition and show the existence of a weak solution.

Multiplicity results for elliptic Kirchhoff-type problems

2017 ◽  
Vol 6 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Sami Baraket ◽  
Giovanni Molica Bisci
Keyword(s):  
Weak Solutions ◽  
Multiple Solutions ◽  
Fractional Operators ◽  
Type Problem ◽  
Small Perturbations ◽  
Multiplicity Results ◽  
Nonlinear Part ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Type Problems

AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.

scholarly journals Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Wei Han ◽  
Yangyang Zhao
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Perturbation Methods ◽  
Dirichlet Boundary ◽  
First Eigenvalue ◽  
Type Problem ◽  
Smooth Bounded Domain ◽  
Kirchhoff Type ◽  
The First Eigenvalue ◽  
Kirchhoff Type Problem

We study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent -a+b∫Ω∇u2dxΔu+u=Q(x)u5+μxα-2u+f(x)(λ/uγ) in Ω,u=0 on ∂Ω, where a,b>0 are constants, Ω⊂R3 is a smooth bounded domain, 0<α<1, λ>0 is a real parameter, γ∈(0,1) is a constant, and 0<μ<aμ1 (μ1 is the first eigenvalue of -Δu=μxα-2u, under Dirichlet boundary condition). Under appropriate assumptions on Q and f, we obtain two positive solutions via the variational and perturbation methods.

scholarly journals Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problems

2014 ◽  
Vol 33 (2) ◽  
pp. 203-217 ◽  
Author(s):  
El Miloud Hssini ◽  
Mohammed Massar ◽  
Najib Tsouli
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Technical Approach ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problems

This paper is concerned with the existence and multiplicity of solutions for a class of $p(x)$-Kirchhoff type equations with Neumann boundary condition. Our technical approach is based on variational methods.

scholarly journals Multiplicity results for the non-homogeneous fractional p -Kirchhoff equations with concave–convex nonlinearities

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150034 ◽  
Author(s):  
Mingqi Xiang ◽  
Binlin Zhang ◽  
Massimiliano Ferrara
Keyword(s):  
Variational Principle ◽  
Differential Operator ◽  
Mountain Pass Theorem ◽  
Type Problem ◽  
Entire Solutions ◽  
Kirchhoff Equations ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Non Local

In this paper, we are interested in the multiplicity of solutions for a non-homogeneous p -Kirchhoff-type problem driven by a non-local integro-differential operator. As a particular case, we deal with the following elliptic problem of Kirchhoff type with convex–concave nonlinearities: a + b ∬ R 2 N | u ( x ) − u ( y ) | p | x − y | N + s p   d x   d y θ − 1 ( − Δ ) p s u = λ ω 1 ( x ) | u | q − 2 u + ω 2 ( x ) | u | r − 2 u + h ( x ) in   R N , where ( − Δ ) p s is the fractional p -Laplace operator, a + b >0 with a , b ∈ R 0 + , λ>0 is a real parameter, 0 < s < 1 < p < ∞ with sp < N , 1< q < p ≤ θp < r < Np /( N − sp ), ω 1 , ω 2 , h are functions which may change sign in R N . Under some suitable conditions, we obtain the existence of two non-trivial entire solutions by applying the mountain pass theorem and Ekeland's variational principle. A distinguished feature of this paper is that a may be zero, which means that the above-mentioned problem is degenerate. To the best of our knowledge, our results are new even in the Laplacian case.

Existence and multiplicity of solutions for an indefinite Kirchhoff-type equation in bounded domains

2016 ◽  
Vol 146 (2) ◽  
pp. 435-448 ◽  
Author(s):  
Juntao Sun ◽  
Tsung-fang Wu
Keyword(s):  
Variational Principle ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Bounded Domains ◽  
Type Problem ◽  
Smooth Bounded Domain ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problem ◽  
Image Position

We study the indefinite Kirchhoff-type problem where Ω is a smooth bounded domain in and . We require that f is sublinear at the origin and superlinear at infinity. Using the mountain pass theorem and Ekeland variational principle, we obtain the multiplicity of non-trivial non-negative solutions. We improve and extend some recent results in the literature.

scholarly journals On 𝓅 ( x ) -Kirchhoff-type equation involving 𝓅 ( x ) -biharmonic operator via genus theor

2020 ◽  
Vol 72 (6) ◽  
pp. 842-851
Author(s):  
S. Taarabti ◽  
Z. El Allali ◽  
K. Ben Haddouch
Keyword(s):  
Weak Solutions ◽  
Variational Approach ◽  
Type Equation ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Genus Theory ◽  
Kirchhoff Type Equation ◽  
Kirchhoff Type Problem

UDC 517.9 The paper deals with the existence and multiplicity of nontrivial weak solutions for the 𝓅 ( x ) -Kirchhoff-type problem, u = Δ u = 0 o n ∂ Ω . By using variational approach and Krasnoselskii’s genus theory, we prove the existence and multiplicity of solutions for the 𝓅 ( x ) -Kirchhoff-type equation.

Sign in / Sign up

Export Citation Format

Share Document