# One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations

## Abstract

We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.

- Authors:

- Institute of Mathematics of National Academy of Sciences of RA (Armenia)
- Armenian National Agrarian University (Armenia)

- Publication Date:

- OSTI Identifier:
- 22771213

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 231; Journal Issue: 2; 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; ASYMPTOTIC SOLUTIONS; INTEGRAL EQUATIONS; NONLINEAR PROBLEMS

### Citation Formats

```
Khachatryan, Kh. A., E-mail: Khach82@rambler.ru, E-mail: Khach82@mail.ru, and Petrosyan, H. S., E-mail: haykuhi25@mail.ru.
```*One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3812-2.

```
Khachatryan, Kh. A., E-mail: Khach82@rambler.ru, E-mail: Khach82@mail.ru, & Petrosyan, H. S., E-mail: haykuhi25@mail.ru.
```*One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations*. United States. doi:10.1007/S10958-018-3812-2.

```
Khachatryan, Kh. A., E-mail: Khach82@rambler.ru, E-mail: Khach82@mail.ru, and Petrosyan, H. S., E-mail: haykuhi25@mail.ru. Tue .
"One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations". United States. doi:10.1007/S10958-018-3812-2.
```

```
@article{osti_22771213,
```

title = {One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations},

author = {Khachatryan, Kh. A., E-mail: Khach82@rambler.ru, E-mail: Khach82@mail.ru and Petrosyan, H. S., E-mail: haykuhi25@mail.ru},

abstractNote = {We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.},

doi = {10.1007/S10958-018-3812-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 2,

volume = 231,

place = {United States},

year = {2018},

month = {5}

}

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