# On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation

## Abstract

We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.

- Authors:

- Perm National Research Polytechnic University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771274

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; 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; BOUNDARY-VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; SINGULARITY

### Citation Formats

```
Plaksina, V. P., E-mail: vpplaksina@list.ru, Plaksina, I. M., E-mail: impl@list.ru, and Plekhova, E. V., E-mail: elvira.plekhova@mail.ru.
```*On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3781-5.

```
Plaksina, V. P., E-mail: vpplaksina@list.ru, Plaksina, I. M., E-mail: impl@list.ru, & Plekhova, E. V., E-mail: elvira.plekhova@mail.ru.
```*On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation*. United States. doi:10.1007/S10958-018-3781-5.

```
Plaksina, V. P., E-mail: vpplaksina@list.ru, Plaksina, I. M., E-mail: impl@list.ru, and Plekhova, E. V., E-mail: elvira.plekhova@mail.ru. Tue .
"On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation". United States. doi:10.1007/S10958-018-3781-5.
```

```
@article{osti_22771274,
```

title = {On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation},

author = {Plaksina, V. P., E-mail: vpplaksina@list.ru and Plaksina, I. M., E-mail: impl@list.ru and Plekhova, E. V., E-mail: elvira.plekhova@mail.ru},

abstractNote = {We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.},

doi = {10.1007/S10958-018-3781-5},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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