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

## Abstract

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.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 22771585

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 228; Journal 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); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Vougalter, V., E-mail: vitali@math.toronto.edu, and Volpert, V., E-mail: volpert@math.univ-lyon1.fr.
```*Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations*. United States: N. p., 2018.
Web. doi:10.1007/S10958-017-3650-7.

```
Vougalter, V., E-mail: vitali@math.toronto.edu, & Volpert, V., E-mail: volpert@math.univ-lyon1.fr.
```*Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations*. United States. doi:10.1007/S10958-017-3650-7.

```
Vougalter, V., E-mail: vitali@math.toronto.edu, and Volpert, V., E-mail: volpert@math.univ-lyon1.fr. Thu .
"Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations". United States. doi:10.1007/S10958-017-3650-7.
```

```
@article{osti_22771585,
```

title = {Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations},

author = {Vougalter, V., E-mail: vitali@math.toronto.edu and Volpert, V., E-mail: volpert@math.univ-lyon1.fr},

abstractNote = {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.},

doi = {10.1007/S10958-017-3650-7},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 228,

place = {United States},

year = {2018},

month = {2}

}

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