Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects

Document Type : research paper


1 Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran

2 Department Pure Mathematics , Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran


Fractional differential equations have been of great interest recently. This is because of both
the intensive development of the theory of fractional calculus itself and the applications of such
constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dynamics
of processes in which sudden, discontinuous jumps occur. For the background, theory and applications
of impulsive differential equations. There have been many approaches to study the existence of solutions of impulsive fractional differential equations, such as fixed point theory, topological degree theory, upper and lower solutions methods and monotone iterative method.
In this paper, we study the existence of solutions for a new class of p-Laplacian fractional
boundary value problem with impulsive effects. By using critical point theory and variational
methods, we give some new criteria to guarantee that the impulsive problem have infinitely
many solutions.


Article Title [فارسی]

وجود جوابهای یک معادله دیفرانسیل کسری جدید p-لاپلاسین با اثر ضربه ای

Authors [فارسی]

  • نعمت‌اله نیامرادی 1
  • عبدالرحمن رازانی 2
1 گروه ریاضی، دانشکده علوم، دانشگاه رازی، کرمانشاه، ایران
2 گروه ریاضی محض، دانشکده علوم پایه، دانشگاه بین‌المللی امام خمینی(ره)، قزوین، ایران
Abstract [فارسی]

معادلات دیفرانسیل با اثر ضربه‌ای از فرایندهای دینامیکی با جهش‌های ناپیوسته رخ خواهد داد. محققین زیادی وجود جواب‌های معادلات دیفرانسی کسری ضربه‌‌ای با استفاده از نظریه نقطه ثابت، نظریه درجه توپولوژیکی، روش جوا‌های بالا و پایین و روش‌های تکراری یکنوا را مورد مطالعه و بررسی قرار داده-اند.
در این مقاله، وجود جواب‌ها برای یک کلاس از معادلات دیفرانسیل کسری p-لاپلاسین جدید با اثر ضربه‌ای را مورد مطالعه قرار خواهیم داد. با استفاده از قضیه نقطه بحرانی و روش‌های تغییراتی نشان خواهیم داد که این معادله دیفراتسل ضربه‌ای بی‌نهایت جواب دارد.

Keywords [فارسی]

  • معادله دیفرانسیل کسری
  • ضربه
  • جواب
  • روش‌های تغییراتی
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