A New Proof of the Existence of Nonzero Weak Solutions of Impulsive Fractional Boundary Value Problems

Asma Alharbi,Rafik Guefaifia,Salah Boulaaras

doi:10.3390/math8050856

Asma Alharbi, Rafik Guefaifia + Show 1 more

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https://doi.org/10.3390/math8050856

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Abstract

The paper deals with the existence of at least two non zero weak solutions to a new class of impulsive fractional boundary value problems via Brezis and Nirenberg’s Linking Theorem. Finally, an example is presented to illustrate our results.

Highlights

The paper deals with the existence of weak solutions to the following boundary value problems for impulsive fractional Hamiltonian differential equations:
The existence of solutions of boundary value problems for Fractional differential equations have widely been studied in many papers and we refer the reader to the papers [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
We can extend the previous mentioned works for proving the existence of at least two non zero weak solutions to a new class of impulsive fractional boundary value problems via Brezis and Nirenberg’s Linking Theorem

Summary

Introduction

The paper deals with the existence of weak solutions to the following boundary value problems for impulsive fractional Hamiltonian differential equations:. The existence of solutions of boundary value problems for Fractional differential equations have widely been studied in many papers and we refer the reader to the papers [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. In [3], the authors created a variable structure and, using the critical point theory, investigated the existence of multiple solutions for a class of fractional advection–dispersion equations derived from symmetric mass flow transmission.

Preliminaries and Assumptions

Mains Result

N L h i

N L 2 2 2

Conclusions

Methods