A new criterion for the existence of multiple solutions in cones

Daniel Franco; Gennaro Infante; Juan Perán

doi:10.1017/S0308210511001016

Abstract

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We provide new sufficient conditions for the existence of multiple fixed points for a map between ordered Banach spaces. An interesting feature of this approach is that we require conditions not on two boundaries, but rather on one boundary and a point with some extra information on the monotonicity of the nonlinearity on a certain set. We apply our results to prove the existence of at least two positive solutions for a nonlinear boundary-value problem that models a thermostat.

Crossref Citations

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

Cabada, Alberto Cid, José Ángel and Infante, Gennaro 2013. New criteria for the existence of non-trivial fixed points in cones. Fixed Point Theory and Applications, Vol. 2013, Issue. 1,

Cabada, Alberto Cid, José Ángel and Infante, Gennaro 2014. A positive fixed point theorem with applications to systems of Hammerstein integral equations. Boundary Value Problems, Vol. 2014, Issue. 1,

Chen, Yi and Tang, Xianhua 2014. The difference between a class of discrete fractional and integer order boundary value problems. Communications in Nonlinear Science and Numerical Simulation, Vol. 19, Issue. 12, p. 4057.

Cabada, Alberto and Saavedra, Lorena 2016. The eigenvalue characterization for the constant sign Green’s functions of ( k , n − k ) $(k,n-k)$ problems. Boundary Value Problems, Vol. 2016, Issue. 1,

Cid, José Ángel and Infante, Gennaro 2017. A non-variational approach to the existence of nonzero positive solutions for elliptic systems. Journal of Fixed Point Theory and Applications, Vol. 19, Issue. 4, p. 3151.

Webb, J. R. L. 2017. New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, Vol. 49, Issue. 3, p. 534.

Cianciaruso, Filomena Infante, Gennaro and Pietramala, Paolamaria 2017. Solutions of perturbed Hammerstein integral equations with applications. Nonlinear Analysis: Real World Applications, Vol. 33, Issue. , p. 317.

Cabada, Alberto Dimitrijevic, Sladjana Tomovic, Tatjana and Aleksic, Suzana 2017. The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions. Mathematical Methods in the Applied Sciences, Vol. 40, Issue. 6, p. 1880.

Cabada, Alberto and Saavedra, Lorena 2018. Existence of solutions for nth-order nonlinear differential boundary value problems by means of fixed point theorems. Nonlinear Analysis: Real World Applications, Vol. 42, Issue. , p. 180.

Cabada, Alberto Cid, José Ángel and López-Somoza, Lucía 2018. Maximum Principles for the Hill's Equation. p. 129.

Figueroa Sestelo, Rubén López Pouso, Rodrigo and Rodríguez López, Jorge 2021. Degree Theory for Discontinuous Operators. Vol. 6, Issue. , p. 25.

Figueroa Sestelo, Rubén López Pouso, Rodrigo and Rodríguez López, Jorge 2021. Degree Theory for Discontinuous Operators. Vol. 6, Issue. , p. 135.

Calamai, Alessandro and Infante, Gennaro 2024. Topological Methods for Delay and Ordinary Differential Equations. Vol. 51, Issue. , p. 141.

Krajščáková, Věra and Tojo, F. Adrián F. 2024. Existence and multiplicity of solutions of Stieltjes differential equations via topological methods. Journal of Fixed Point Theory and Applications, Vol. 26, Issue. 1,

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A new criterion for the existence of multiple solutions in cones

Abstract

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