Self referred equations with an integral boundary condition
-
Giacomo Chiriatti
and
Eduardo Pascali
Abstract
In this note, we study three differential problems with a dynamic, which are be represented by a self referred equation and a boundary condition, which are expressed as an integral constraint. We prove that under certain assumptions, there exists at least one solution of for all of these problems by using Schauder’s fixed point theorem. In the end, we propose briefly some open problems.
Communicated by Michal Fečkan
References
[1] Eder, E.: The functional-differential equation ∂tx(t) = x(x(t)), J. Differential Equations 54(3) (1984), 390–400.10.1016/0022-0396(84)90150-5Search in Google Scholar
[2] Fichera, G.: Having a long memory creates serious problems, Arch. Ration. Mech. Anal. 2 (1979), 101–112.10.1007/BF00250347Search in Google Scholar
[3] Fichera, G.: Analytic problems of materials with memory in theoretical and applied mechanics. In: Proc. 15th Internat. Congr., Univ. Toronto, Toronto, Ont., 1980, 223–230.Search in Google Scholar
[4] Mangino, E. M.—Pascali, E.: Boundary value problems with an integral constraint, Electron. J. Differential Equations 257 (2015), 1–11.Search in Google Scholar
[5] Miranda, M., Jr.—Pascali, E.: On a type of evolution of self-referred and hereditary phenomena, Aequationes Math. 71 (2006), 253–268.10.1007/s00010-005-2821-7Search in Google Scholar
[6] Miranda, M., Jr.—Pascali, E.: On a class of differential equations with self-reference, Rend. Mat. Appl. (7) 25 (2005), 155–164.Search in Google Scholar
[7] Miranda, M., Jr.—Pascali, E.: Other classes of self-referred equations, Note Mat. 29(1) (2009), 61–72.Search in Google Scholar
[8] Rudin, W.: Functional Analysis, 2nd ed., McGraw-Hill Science, 1991.Search in Google Scholar
[9] Tuan, N. M.—Nguyen, L. T. T.: On solutions of a system of hereditary and self referred partial differential equations, Numer. Algorithms 55 (2010), 101–113.10.1007/s11075-009-9360-6Search in Google Scholar
[10] Van Le, U.—Nguyen, L. T. T.: Existence of solutions to a self-referred and hereditary system of differential equations, Electron. J. Differential Equations 7 (2008), 1–7.Search in Google Scholar
[11] Volterra, V.: Opere Matematiche: Memorie e Note, Vol. 3, 1900–1913, Accademia Nazionale dei Lincei, Roma, 1957.Search in Google Scholar
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Articles in the same Issue
- Algebraic structures formalizing the logic of effect algebras incorporating time dimension
- Walks on tiled boards
- Composition on FLew-algebras
- On high power sums of a hybrid arithmetic function
- On indices of quintic number fields defined by x5 + ax + b
- Note on fundamental system of solutions to the differential equations (D2 − 2Dα + α2 ± β2) y = 0
- Several sharp inequalities involving (hyperbolic) tangent, tanc, cosine, and their reciprocals
- A new Approach of Generalized Fractional Integrals in Multiplicative Calculus and Related Hermite–Hadamard-Type Inequalities with Applications
- On a periodic problem for super-linear second-order ODEs
- Existence and Uniqueness of Solutions for Fractional Dynamic Equations with Impulse Effects
- Periodic Solutions for Conformable Non-autonomous Non-instantaneous Impulsive Differential Equations
- Self referred equations with an integral boundary condition
- Approximation by matrix means of double Vilenkin-Fourier series
- Maps on self-adjoint operators preserving some relations related to commutativity
- Chains in the Rudin-Frolík order
- Relative versions of first and second countability in hyperspaces
- Proportion estimation in multistage pair ranked set sampling
- The Marshall-Olkin Extended Gamma Lindley distribution: Properties, characterization and inference
