Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case

Alberto Boscaggin; Guglielmo Feltrin; Fabio Zanolin

doi:10.1017/S0308210515000621

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the periodic and Neumann boundary-value problems associated with the second-order nonlinear differential equation

where is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when

and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Boscaggin, Alberto and Garrione, Maurizio 2016. Positive solutions to indefinite Neumann problems when the weight has positive average. Discrete and Continuous Dynamical Systems, Vol. 36, Issue. 10, p. 5231.

Feltrin, Guglielmo and Zanolin, Fabio 2017. Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree. Journal of Differential Equations, Vol. 262, Issue. 8, p. 4255.

Xu, Man and Ma, Ruyun 2018. Discrete Neumann boundary value problem for a nonlinear equation with singular ϕ-Laplacian. Advances in Difference Equations, Vol. 2018, Issue. 1,

Boscaggin, Alberto and Feltrin, Guglielmo 2018. Positive subharmonic solutions to nonlinear ODEs with indefinite weight. Communications in Contemporary Mathematics, Vol. 20, Issue. 01, p. 1750021.

Feltrin, Guglielmo and Sovrano, Elisa 2018. An indefinite nonlinear problem in population dynamics: high multiplicity of positive solutions. Nonlinearity, Vol. 31, Issue. 9, p. 4137.

Feltrin, Guglielmo 2018. Positive subharmonic solutions to superlinear ODEs with indefinite weight. Discrete & Continuous Dynamical Systems - S, Vol. 11, Issue. 2, p. 257.

Sovrano, Elisa 2018. A negative answer to a conjecture arising in the study of selection–migration models in population genetics. Journal of Mathematical Biology, Vol. 76, Issue. 7, p. 1655.

Jiao, Lishuai and Zhang, Xuemei 2018. A class of second-order nonlocal indefinite impulsive differential systems. Boundary Value Problems, Vol. 2018, Issue. 1,

Hakl, Robert and Zamora, Manuel 2019. Existence and Multiplicity of Periodic Solutions to Indefinite Singular Equations Having a Non-monotone Term with Two Singularities. Advanced Nonlinear Studies, Vol. 19, Issue. 2, p. 317.

Feltrin, Guglielmo and Gidoni, Paolo 2020. Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model. Nonlinear Analysis: Real World Applications, Vol. 54, Issue. , p. 103108.

Boscaggin, Alberto Feltrin, Guglielmo and Sovrano, Elisa 2020. High Multiplicity and Chaos for an Indefinite Problem Arising from Genetic Models. Advanced Nonlinear Studies, Vol. 20, Issue. 3, p. 675.

Boscaggin, Alberto and Feltrin, Guglielmo 2020. Positive periodic solutions to an indefinite Minkowski-curvature equation. Journal of Differential Equations, Vol. 269, Issue. 7, p. 5595.

Boscaggin, Alberto and Feltrin, Guglielmo 2020. Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight. Nonlinear Analysis, Vol. 196, Issue. , p. 111807.

Amster, Pablo Benevieri, Pierluigi and Haddad, Julián 2021. Periodic positive solutions of superlinear delay equations via topological degree. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 379, Issue. 2191, p. 20190373.

Boscaggin, Alberto Feltrin, Guglielmo and Zanolin, Fabio 2023. Positive solutions for a Minkowski-curvature equation with indefinite weight and super-exponential nonlinearity. Communications in Contemporary Mathematics, Vol. 25, Issue. 04,

Zhao, Zhongzi and Ma, Ruyun 2023. Global bifurcation of positive solutions of a quasilinear indefinite Neumann problem in some FLRW spacetimes. Journal of Mathematical Physics, Vol. 64, Issue. 7,

Yang, Hujun and Han, Xiaoling 2023. Existence and Uniqueness of Periodic Solutions for a Class of Higher Order Differential Equations. Mediterranean Journal of Mathematics, Vol. 20, Issue. 5,

Ma, Ruyun Zhao, Zhongzi and Su, Xiaoxiao 2024. Global structure of positive and sign-changing periodic solutions for the equations with Minkowski-curvature operator. Advanced Nonlinear Studies, Vol. 24, Issue. 3, p. 775.

Ma, Ruyun Yang, Lijuan and Zhang, Yali 2024. Global structure of positive solutions for p-Laplacian Neumann problem with indefinite weight. Computational and Applied Mathematics, Vol. 43, Issue. 3,

Su, Xiaoxiao Yan, Meng and Ma, Ruyun 2024. GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR FIRST-ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS WITH INDEFINITE WEIGHT. Journal of Applied Analysis & Computation, Vol. 14, Issue. 1, p. 119.

Download full list

Article contents

Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case

Extract

Keywords

MSC classification

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case

Extract

Keywords

MSC classification

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests