i look for a list of theoretical topics in differential equation not necessarily active research topics. the topics that is the in field of a concret math and is not differential equation applications.
Hi Dear Behrad Mahboobi
You may choice the topic which is given below:
Developments of new methodologies for solving nonlinear differential equations.
Best regards
Dr. Alal Hosen
Fundamental system of solutions, Existence and uniqueness of the solutions, Bessel's, Legendre's etc are the topics included in ODE(s).
Fractional calculus has emerged as one of the most important
interdisciplinary subjects during the last four decades mainly due to its applications in various fields of science and engineering. Therefore the topic of " fractional calculus integral and differential equations of fractional order " is a very interesting topic
Dear Behrad,
Most of differential equations are equivalent to the corresponding integral equations. The latter ones are more easy to handle. One of the reasons is that most of integral operators are compact operators. About such operators more information on their spectrum, and other information is known as well. It is not the case of differential operators, which are unbounded. Moreover, iterative methods work more easily for integral operators (successive approximation (contraction principle), Newton's method and others).
Sincerely, Octav
Well, classical research topics include asymptotic behavior of solutions, stability, existence and uniqueness of solutions in general and existence of bounded, oscillatory, non-oscillatory, or periodic in particular, asymptotic expansions for solutions, bifurcations, existence of solutions to boundary value problems, to mention a few. It might help to look at some classical papers by prominent researchers like Hartman, Levinson, LaSalle, Wintner and browse papers at published in 50s-80s https://www.jstor.org/ to have a feeling of classic research in ODEs.
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