Existence of Weak Solutions to a Kind of System of Fractional Semi-Linear Fredholm-Volterra Boundary Value Problem
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
E. Shivanian
1
(Department of Mathematics, Imam Khomeini International
University, Qazvin, Iran.)
کلید واژه: Variational method, Critical point theory, System of fractional semi-linear Fredholm-Volterra integro-differential equations, Weak solution, Dirichlet condition,
چکیده مقاله :
‎This article is devoted to study the weak solutions of a class of nonlinear system of fractional boundary value problems including both Volterra and Fredholm linear integral terms. This system of fractional semi-linear Fredholm-Volterra integro-differential equations does have a gradient of a nonlinear source term as well. We apply the critical point theory and the variational structure to prove the existence of at least three distinct weak solutions to the system. Furthermore, it is presented an example to verify the legitimacy and applicability of the ‎theory.‎
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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