Temat: rozwiązanie całkowe - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Weak solutions of fractional order differential equations via Volterra-Stieltjes integral operator
Autorzy:: El-Sayed, A. M. A.
El-Sayed, W. G.
Abd El-Mowla, A. A. H.
Powiązania:: https://bibliotekanauki.pl/articles/357800.pdf
Data publikacji:: 2017
Wydawca:: Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:: weak solution
mild solution
weakly Riemann-Stieltjes integral
function of bounded variation
Banach space
rozwiązanie całkowe
całka Riemanna-Stieltjesa
funkcja o ograniczonej zmienności
przestrzeń Banacha
Opis:: The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type in reflexive Banach spaces.
Źródło:: Journal of Mathematics and Applications; 2017, 40; 85-96
1733-6775
2300-9926
Pojawia się w:: Journal of Mathematics and Applications
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On the number of positive solutions to a class of integral equations
Autorzy:: Wang, L.
Yu, W.
Zhang, L.
Powiązania:: https://bibliotekanauki.pl/articles/206271.pdf
Data publikacji:: 2003
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie całkowe
rozwiązanie dodatnie
integral equations
positive solutions
complete discrimination system for polynomials
number of solutions
Opis:: By using the complete discrimination system for polynomials, we study the number of positive solutions in C[0,1] to the integral equation phi(x) = integral[...] k(x,y)phi^n(y)dy, where k(x,y) = phi1(x)phi1(y)+phi2(x)phi2(y),[phi]i(x) > 0,[phi]i(y) > 0,0 < x,y < 1,i = 1,2, are continuous functions on [0,1], n is a positive integer. We prove the following results: when n = 1, either there does not exist, or there exist infinitely many positive solutions in C[0,1]; when n [is greater than or equal] 2, there exist at least 1, at most n + 1 positive solutions in C[0,1]. Necessary and sufficient conditions are derived for the cases: 1) n = 1, there exist positive solutions; 2) n [is greater than or equal to] 2, there exist exactly m (m belongs to {1,2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
Źródło:: Control and Cybernetics; 2003, 32, 2; 383-395
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Optimal Shape Design for Elliptic Equations Via Bie-Methods
Autorzy:: Eppler, K.
Powiązania:: https://bibliotekanauki.pl/articles/911209.pdf
Data publikacji:: 2000
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: rozwiązanie podstawowe
równanie całkowe
optimal shape design
fundamental solution
boundary integral equation
first-order necessary condition
Opis:: A special description of the boundary variation in a shape optimization problem is investigated. This, together with the use of a potential theory for the state, result in natural embedding of the problem in a Banach space. Therefore, standard differential calculus can be applied in order to prove the Frechet-differentiability of the cost function for appropriately chosen data (sufficiently smooth). Moreover, necessary optimality conditions are obtained in a similar way as in other approaches, and are expressed in terms of an adjoint state for more regular data.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2000, 10, 3; 487-516
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

Artykuł

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