<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1. </p></abstract>

In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution...

The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

Published Online: Mar 31, 2018

Page range: 5 - 41

Received: Dec 20, 2016

Accepted: Sep 20, 2017

DOI: https://doi.org/10.2478/auom-2018-0001

Keywords
Kirchhoff-type elliptic problems, Rabinowitz-type global bifurcation theory, Sub-supersolution method, Existence, Uniqueness

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

Published Online: Mar 31, 2018

Page range: 5 - 41

Received: Dec 20, 2016

Accepted: Sep 20, 2017

DOI: https://doi.org/10.2478/auom-2018-0001

KeywordsKirchhoff-type elliptic problems, Rabinowitz-type global bifurcation theory, Sub-supersolution method, Existence, Uniqueness

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Kirchhoff-type elliptic problems, Rabinowitz-type global bifurcation theory, Sub-supersolution method, Existence, Uniqueness