Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations

Journal Article · Thu Feb 15 00:00:00 EST 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-017-3650-7· OSTI ID:22771585

Vougalter, V., E-mail: [e-mail] ^[1]; Volpert, V., E-mail: [e-mail] ^[2]

---

1. University of Toronto (Canada)
2. University Lyon 1, Institute Camille Jordan, UMR 5208 CNRS (France)

We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H{sup 2} spaces. It is shown that, under reasonable technical conditions, the convergence in L{sup 1} of the integral kernels implies the existence and convergence in H{sup 2} of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.

• OSTI ID: 22771585
• Journal Information: Journal of Mathematical Sciences, Vol. 228, Issue 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONVERGENCE
DIFFERENTIAL OPERATORS
DIFFUSION EQUATIONS
INTEGRALS
INTEGRO-DIFFERENTIAL EQUATIONS
KERNELS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE