Schauder's fixed-point theorem: new applications and a new version for discontinuous operators

DOI10.1186/1687-2770-2012-92zbMath1301.47073OpenAlexW2164271510WikidataQ59288515 ScholiaQ59288515MaRDI QIDQ384341

Rodrigo López Pouso

Publication date: 27 November 2013

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2012-92

zbMATH Keywords

fixed-point theoremdiscontinuous operatorsdiscontinuous differential equationsSchauder's theorem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Fixed-point theorems (47H10) Discontinuous ordinary differential equations (34A36)

Related Items (13)

A Schauder-type theorem for discontinuous operators with applications to second-order BVPs ⋮ Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators ⋮ A unified variational approach to discontinuous differential equations ⋮ Fixed point index for discontinuous operators and fixed point theorems in cones with applications ⋮ A version of Krasnosel'skiĭ's compression-expansion fixed point theorem in cones for discontinuous operators with applications ⋮ New fixed point theorem for discontinuous operators in cones and applications ⋮ Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result ⋮ Unnamed Item ⋮ Fixed point index theory for decomposable multivalued maps and applications to discontinuous \(\phi\)-Laplacian problems ⋮ Compression-expansion fixed point theorems for decomposable maps and applications to discontinuous \(\phi\)-Laplacian problems ⋮ Existence and multiplicity results for second-order discontinuous problems via non-ordered lower and upper solutions ⋮ Positive solutions of a discontinuous one-dimensional beam equation ⋮ Positive solutions for φ-Laplace equations with discontinuous state-dependent forcing terms

Cites Work

• Second-order functional differential equations with past, present and future dependence
• Minimal and maximal solutions to second-order boundary value problems with state-dependent deviating arguments
• Second order problems with functional conditions including Sturm-Liouville and multipoint conditions
• Extremal solutions of a discontinuous scalar differential equation
• Ordinary differential equations and systems with time-dependent discontinuity sets
• On the Cauchy problem for first order discontinuous ordinary differential equations

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