وجود جوابهای ضعیف برای یک سیستم مقدار مرزی فراکشنالی نیمه-خطی ولترا – فردهلم

Subject Areas : International Journal of Industrial Mathematics

الیاس شیوانیان ¹ ( گروه ریاضی، دانشگاه بین المللی امام خمینی، قزوین، ایران. )

Received: 2020-10-20 Accepted : 2021-06-25 Published : 2022-04-01

Keywords: جواب ضعیف, تئوری نقطه بحرانی, شرایط دیریکله, روش تغییراتی, سیستم معادلات انتگرال-دیفرانسیل نیمه خطی کسری,

Abstract :

این مقاله به مطالعه جوابهای های ضعیف یک رده از سیستم غیر خطی از مسایل مقدار مرزی کسری شامل ترم های انتگرال خطی ولترا و فردهلم می پردازد. این سیستم معادلات انتگرال-دیفرانسیل نیمه خطی کسری ولترا-فردهلم همچنین دارای یک ترم گرادیان از یک جمله غیر خطی هست. ما تئوری نقطه بحرانی و ساختار تغییراتی را برای اثبات وجود حداقل سه جواب ضعیف مجزا برای سیستم اعمال می کنیم. برای این منظور، ما از قضیه معروفی درباره ساخت مجموعه نقاط بحرانی از تابعکها با شرط فشردگی ضعیف بهره می بریم. علاوه بر این، مثالی برای تأیید آنالیز و کاربرد نظریه ارائه شده، آورده شده است.

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