Search
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.
Citations
-
1
CrossRef
-
0
Web of Science
-
0
Scopus
Authors (3)
Cite as
Full text
download paper
downloaded 50 times
- Publication version
- Accepted or Published Version
- License
-
open in new tab
Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Fixed Point Theory and Applications
no. 2019,
edition 1,
pages 1 - 9,
ISSN: 1687-1820 - 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
- Bibliography: test
-
show (15) hide
- Bereanu, C., Mawhin, J.: Nonhomogeneous boundary value problems for some nonlinear equations with singular φ-Laplacian. J. Math. Anal. Appl. 352(1), 218-233 (2009) open in new tab
- Cabada, A., Dimitrov, N.D.: Existence results for singular ϕ-Laplacian problems in presence of lower and upper solutions. Anal. Appl. 13(2), 135-148 (2015) open in new tab
- Kelevedjiev, P.S., Tersian, S.A.: The barrier strip technique for a boundary value problem with p-Laplacian. Electron. J. Differ. Equ. 2013, 28 (2013) open in new tab
- Kelevedjiev, P., Bojerikov, S.: On the solvability of a boundary value problem for p-Laplacian differential equations. Electron. J. Qual. Theory Differ. Equ. 2017, 9 (2017) open in new tab
- Ma, R.Z.L., Liu, R.: Existence results for nonlinear problems with φ-Laplacian. Electron. J. Qual. Theory Differ. Equ. 2015, 22 (2015) open in new tab
- Mawhin, J.: Homotopy and nonlinear boundary value problems involving singular φ-Laplacians. J. Fixed Point Theory Appl. 13(1), 25-35 (2013) open in new tab
- Rachůnková, I., Staněk, S., Tvrdý, M.: Chap. 7. Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equations. In: Handbook of Differential Equations: Ordinary Differential Equations, vol. 3, pp. 607-723. North-Holland, Amsterdam (2006) open in new tab
- Staněk, S.: Positive and dead-core solutions of two-point singular boundary value problems with ϕ-Laplacian. Adv. Differ. Equ. 2010, 17 (2010) open in new tab
- Wang, X., Liu, Q., Qian, D.: Existence and multiplicity results for some nonlinear problems with singular φ-Laplacian via a geometric approach. Bound. Value Probl. 2016, 27 (2016) open in new tab
- Bernstein, S.: Sur les équations du calcul des variations. Ann. Sci. Éc. Norm. Supér. (3) 29, 431-485 (1912) open in new tab
- Granas, A., Guenther, R., Lee, J.: On a theorem of S. Bernstein. Pac. J. Math. 74(1), 67-82 (1978) open in new tab
- Baxley, J.V.: Nonlinear second order boundary value problems: an existence-uniqueness theorem of S. N. Bernstein. In: Ordinary Differential Equations and Operators, to F. V. Atkinson, Proc. Symp., Dundee/Scotl. 1982. Lect. Notes Math., vol. 1032, pp. 9-16 (1983) open in new tab
- Frigon, M., O'Regan, D.: On a generalization of a theorem of S. Bernstein. Ann. Pol. Math. 48, 297-306 (1988) open in new tab
- Krasnoselskiȋ, M.A., Rutickiȋ, J.B.: Convex Functions and Orlicz Spaces. Noordhoff, Groningen (1961)
- Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2010) open in new tab
- Sources of funding:
- Verified by:
- Gdańsk University of Technology
seen 241 times