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2024 | OriginalPaper | Chapter

Robin Boundary Value Problem for Some Nonlinear Nonlocal Elliptic Partial Differential Equations

Authors : Petar Popivanov, Angela Slavova

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

This paper deals with Robin type boundary value problems for the mean field equation in the unit circle and for a nonlocal autonomous second order ordinary differential equation with cubic nonlinearity in the unit interval. The radial solutions in the first case and the classical solutions in the second one are written into explicit form. The real- valued spectral parameter can be bounded and unbounded and participates in the formulae for the corresponding solutions.

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previous chapter Improved Hardy Inequality with Logarithmic Term
next chapter The Ericksen-Leslie System for Data on a Plane
Literature
1.
J. Guo, N. Kavallaris, Chi Wang, Ch. Yu. Bifurcation diagram of a Robin boundary value problem arising in MEMS, Hiroshima Math.J., v.52, 2022, 311-320.
2.
E. Kamke. Differentialgleichungen. Lösungsmethoden und Lösungen, I: Gewonliche Differentialgleichungen, Leipzig, 1959.
3.
L. Onsager. Statistical hydrodynamics. Nuovo Cimento (9),6:2 - Supplemento, 1949, 272-287.
4.
P.Popivanov, A. Slavova. Radial and nonradial solutions for local and nonlocal Liouville type equations, AIP Conference Proceedings 2459, 030042 (2022).
Metadata
Title
Robin Boundary Value Problem for Some Nonlinear Nonlocal Elliptic Partial Differential Equations
Authors
Petar Popivanov
Angela Slavova
Copyright Year
2024
Book
New Trends in the Applications of Differential Equations in Sciences

Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-53212-2_7

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