# Bernstein-type theorem for ϕ-Laplacian - Publication - MOST Wiedzy

## Bernstein-type theorem for ϕ-Laplacian

### Abstract

In this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth condition. Our result is based on a priori bounds for the solution and homotopical invariance of the Leray–Schauder degree.

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### Details

Category:
Magazine publication
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
Fixed Point Theory and Applications no. 2019, edition 1, pages 1 - 9,
ISSN: 1687-1812
Language:
English
Publication year:
2019
Bibliographic description:
Maksymiuk J., Ciesielski J., Starostka M.: Bernstein-type theorem for ϕ-Laplacian// Fixed Point Theory and Applications. -Vol. 2019, iss. 1 (2019), s.1-9
DOI:
Digital Object Identifier (open in new tab) 10.1186/s13663-018-0651-2

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