scholarly journals Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p-Laplacian

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 106
Author(s):  
Danyang Kang ◽  
Cuiling Liu ◽  
Xingyong Zhang
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Lower Bound ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Type System ◽  
Large Parameter ◽  
Local Conditions ◽  
Kirchhoff Type

In this paper, we investigate the existence of solutions for a class of p-Laplacian fractional order Kirchhoff-type system with Riemann–Liouville fractional derivatives and a parameter λ . By mountain pass theorem, we obtain that system has at least one non-trivial weak solution u λ under some local conditions for each given large parameter λ . We get a concrete lower bound of the parameter λ , and then obtain two estimates of weak solutions u λ . We also obtain that u λ → 0 if λ tends to ∞. Finally, we present an example as an application of our results.

scholarly journals Nontrivial Solutions for a Class of p-Kirchhoff Dirichlet Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xian Hu ◽  
Yong-Yi Lan
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Variational Method ◽  
Critical Point ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Nontrivial Solutions ◽  
Kirchhoff Type

This paper is devoted to the following p-Kirchhoff type of problems −a+b∫Ω∇updxΔpu=fx,u,x∈Ωu=0,x∈∂Ω with the Dirichlet boundary value. We show that the p-Kirchhoff type of problems has at least a nontrivial weak solution. The main tools are variational method, critical point theory, and mountain-pass theorem.

scholarly journals Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

2019 ◽  
Vol 38 (4) ◽  
pp. 31-50
Author(s):  
M. Bagheri ◽  
Ghasem A. Afrouzi
Keyword(s):  
Local Minimum ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Hardy Potential ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Minimum Theorem

In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

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.

scholarly journals Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
N. Nyamoradi ◽  
Y. Zhou ◽  
E. Tayyebi ◽  
B. Ahmad ◽  
A. Alsaedi
Keyword(s):  
Variational Methods ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Nontrivial Solutions ◽  
Nonlinear Schrödinger ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Left And Right

We study the existence of solutions for time fractional Schrödinger-Kirchhoff type equation involving left and right Liouville-Weyl fractional derivatives via variational methods.

The existence of solutions with prescribed L2-norm for Kirchhoff type system

2017 ◽  
Vol 58 (4) ◽  
pp. 041502
Author(s):  
Xiaofei Cao ◽  
Junxiang Xu ◽  
Jun Wang
Keyword(s):  
Existence Of Solutions ◽  
Type System ◽  
Kirchhoff Type ◽  
L2 Norm

scholarly journals Nontrivial Solutions of the Kirchhoff-Type Fractional p-Laplacian Dirichlet Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Taiyong Chen ◽  
Wenbin Liu ◽  
Hua Jin
Keyword(s):  
Dirichlet Problem ◽  
Fractional Derivative ◽  
Weak Solutions ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this article, we consider the new results for the Kirchhoff-type p-Laplacian Dirichlet problem containing the Riemann-Liouville fractional derivative operators. By using the mountain pass theorem and the genus properties in the critical point theory, we get some new results on the existence and multiplicity of nontrivial weak solutions for such Dirichlet problem.

scholarly journals Existence of solutions for a class of strongly coupled $p(x)-$ laplacian system

2018 ◽  
Vol 36 (4) ◽  
pp. 183-195
Author(s):  
Eada Ahmed Al Zahrani ◽  
Mohamed Ali Mourou ◽  
Kamel Saoudi
Keyword(s):  
Weak Solution ◽  
Nonlinear System ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Main Argument ◽  
Strongly Coupled ◽  
Laplacian Operators

We prove the existence of a non trivial weak solution for certain class of strongly coupled nonlinear system containing the ($p(x)-q(x))$ laplacian operators using as main argument the mountain pass Theorem of {\sc Ambrosetti-Rabinowitz}.

scholarly journals Existence of solution for Dirichlet problem with p(x)-Laplacien

2014 ◽  
Vol 33 (2) ◽  
pp. 243-250
Author(s):  
Nimoun Moussaoui ◽  
L. Elbouyahyaoui
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Mountain Pass Theorem ◽  
Existence Of Solution ◽  
Mountain Pass

In this paper we study an elliptic equation involving the p(x)-Laplacien operateur, for that equation we prove the existence of a non trivial weak solution. The proof relies on simple variational arguments based on the Mountain-Pass theorem.

Existence results for a Kirchhoff type equation in Orlicz–Sobolev spaces

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
EL Miloud Hssini ◽  
Najib Tsouli ◽  
Mustapha Haddaoui
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Nonlocal Problems ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

AbstractIn this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

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