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The Fučík Spectrum for One Dimensional Kreĭn–Feller Operators

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Abstract

In this article we study the Fučík spectrum for one dimensional Kreĭn–Feller operators, also known as measure-geometric Laplacians. We show the existence of a sequence of continuous and monotonic curves, and hyperbolic curves restricting their location. As a by-product, we give a different characterization of the eigenvalues of Kreĭn–Feller operators using nonlinear variational tools, and we show that they coincide with the ones obtained with the linear theory for compact operators in Hilbert spaces.

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Funding

This work was partially supported by grants PIP 11220200102851CO, CONICET, and UBACYT 20020170100445BA.

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Authors and Affiliations

  1. Departamento de Matemática and Instituto de Investigaciones Matemáticas Luis A. Santaló, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón I., Av. Cantilo s/n (1428), Buenos Aires, Argentina

    Martina Oviedo & Juan Pablo Pinasco

  2. Facultad de Ciencias Exactas y Naturales, Universidad de La Pampa, Av Uruguay 151 (6300), Santa Rosa, La Pampa, Argentina

    Cristian Scarola

Authors
  1. Martina Oviedo
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  2. Juan Pablo Pinasco
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  3. Cristian Scarola
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All authors contributed to the work. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Juan Pablo Pinasco.

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Oviedo, M., Pinasco, J.P. & Scarola, C. The Fučík Spectrum for One Dimensional Kreĭn–Feller Operators. Mediterr. J. Math. 20, 133 (2023). https://doi.org/10.1007/s00009-023-02357-7

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  • DOI: https://doi.org/10.1007/s00009-023-02357-7

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