On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ 3 and ℝ 4 are given to illustrate the theoritical results.

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Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽

10.3390/math8040475 ◽

2020 ◽

Vol 8 (4) ◽

pp. 475 ◽

Cited By ~ 6

Author(s):

Fares Kamache ◽

Rafik Guefaifia ◽

Salah Boulaaras ◽

Asma Alharbi

Keyword(s):

Variational Methods ◽

Critical Point ◽

Weak Solutions ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Value Systems ◽

Existence Of Weak Solutions ◽

New Class ◽

Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

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Existence of Solutions for Fractional Boundary Value Problem with Nonlinear Derivative Dependence

Abstract and Applied Analysis ◽

10.1155/2014/812910 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

Wenzhe Xie ◽

Jing Xiao ◽

Zhiguo Luo

Keyword(s):

Boundary Value Problem ◽

Variational Methods ◽

Fractional Derivatives ◽

Existence Of Solutions ◽

Boundary Value ◽

Iterative Technique ◽

Fractional Boundary Value Problem ◽

Left And Right

We investigate the existence of solutions for fractional boundary value problem including both left and right fractional derivatives by using variational methods and iterative technique.

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Three weak solutions for a class of Neumann boundary value systems involving the (p1,...,pn)-Laplacian

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v38i5.41022 ◽

2019 ◽

Vol 38 (5) ◽

pp. 175-185

Author(s):

Armin Hadjian

Keyword(s):

Variational Methods ◽

Weak Solutions ◽

Boundary Value ◽

Neumann Boundary ◽

Value Systems ◽

Uniformly Bounded

In this paper, we establish the existence of two intervals ofpositive real parameters $\lambda$ for which a class of Neumannboundary value equations involving the (p1,...,pn)-Laplacianadmits three weak solutions, whose norms are uniformly bounded withrespect to $\lambda$ belonging to one of the two intervals. Theapproach is based on variational methods.

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Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2017/9281049 ◽

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.

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EXISTENCE OF 3-WEAK SOLUTIONS FOR A NEW CLASS OF AN OVERDETERMINED SYSTEM OF FRACTIONAL PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽

10.1142/s0218348x20400368 ◽

2020 ◽

Vol 28 (08) ◽

pp. 2040036 ◽

Cited By ~ 3

Author(s):

SALAH BOULAARAS ◽

RAFIK GUEFAIFIA ◽

ASMA ALHARBI ◽

BAHRI CHERIF

Keyword(s):

Differential Equations ◽

Variational Methods ◽

Critical Point ◽

Differential System ◽

Point Theorem ◽

Weak Solutions ◽

Overdetermined System ◽

Critical Point Theorem ◽

New Class

The paper deals with the existence of three different weak solutions of [Formula: see text] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

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A variational approach for fractional boundary value systems depending on two parameters

Filomat ◽

10.2298/fil1802517a ◽

2018 ◽

Vol 32 (2) ◽

pp. 517-530

Author(s):

Ghasem Afrouzi ◽

Samad Kolagar ◽

Armin Hadjian ◽

Jiafa Xu

Keyword(s):

Variational Methods ◽

Critical Point ◽

Critical Point Theory ◽

Variational Approach ◽

Boundary Value ◽

Point Theory ◽

Value Systems ◽

Infinitely Many Solutions ◽

Two Parameters

In this paper, we prove the existence of infinitely many solutions to nonlinear fractional boundary value systems, depending on two real parameters. The approach is based on critical point theory and variational methods. We also give an example to illustrate the obtained results.

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The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0102 ◽

2019 ◽

Vol 20 (3-4) ◽

pp. 361-371

Author(s):

Dongping Li ◽

Fangqi Chen ◽

Yukun An

Keyword(s):

Variational Methods ◽

Boundary Value Problems ◽

Critical Point ◽

Point Theorem ◽

Weak Solutions ◽

Variational Approach ◽

Dirichlet Boundary ◽

Coupled Systems ◽

Critical Point Theorem ◽

Two Parameters

AbstractIn this paper, by using variational methods and a critical point theorem due to Bonanno and Marano, the existence of at least three weak solutions is obtained for a class of p-Laplacian type nonlinear fractional coupled systems depending on two parameters. Two examples are given to illustrate the applications of our main results.

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Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

Advances in Difference Equations ◽

10.1186/s13662-020-03154-2 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Shuqi Wang ◽

Zhanbing Bai

Keyword(s):

Boundary Value Problem ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Boundary Value ◽

Contraction Mapping Principle ◽

Uniqueness Of Solutions ◽

Novel Approach ◽

Banach Contraction ◽

Left And Right ◽

Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

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