Notes on the Fučík spectrum and the mixed boundary value problem
Commentationes Mathematicae Universitatis Carolinae (2012)
- Volume: 53, Issue: 4, page 615-627
- ISSN: 0010-2628
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topHonzlová Exnerová, Vendula. "Notes on the Fučík spectrum and the mixed boundary value problem." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 615-627. <http://eudml.org/doc/252522>.
@article{HonzlováExnerová2012,
abstract = {The paper is devoted to the study of the properties of the Fučík spectrum. In the first part, we analyse the Fučík spectra of the problems with one second order ordinary differential equation with Dirichlet, Neumann and mixed boundary conditions and we present the explicit form of nontrivial solutions. Then, we discuss the problem with two second order differential equations with mixed boundary conditions. We show the relation between the Dirichlet boundary value problem and mixed boundary value problem; using results of E. Massa and B. Ruf, we derive some properties of the Fučík spectrum of the mixed boundary value problem. Finally, we introduce a new proof of the closedness of the Fučík spectrum and a lemma about convergence of the corresponding nontrivial solutions.},
author = {Honzlová Exnerová, Vendula},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fučík spectrum; system of ordinary differential equations of the second order; Dirichlet; Neumann and mixed boundary conditions; spectrum; Neumann boundary condition; mixed boundary conditions},
language = {eng},
number = {4},
pages = {615-627},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on the Fučík spectrum and the mixed boundary value problem},
url = {http://eudml.org/doc/252522},
volume = {53},
year = {2012},
}
TY - JOUR
AU - Honzlová Exnerová, Vendula
TI - Notes on the Fučík spectrum and the mixed boundary value problem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 615
EP - 627
AB - The paper is devoted to the study of the properties of the Fučík spectrum. In the first part, we analyse the Fučík spectra of the problems with one second order ordinary differential equation with Dirichlet, Neumann and mixed boundary conditions and we present the explicit form of nontrivial solutions. Then, we discuss the problem with two second order differential equations with mixed boundary conditions. We show the relation between the Dirichlet boundary value problem and mixed boundary value problem; using results of E. Massa and B. Ruf, we derive some properties of the Fučík spectrum of the mixed boundary value problem. Finally, we introduce a new proof of the closedness of the Fučík spectrum and a lemma about convergence of the corresponding nontrivial solutions.
LA - eng
KW - Fučík spectrum; system of ordinary differential equations of the second order; Dirichlet; Neumann and mixed boundary conditions; spectrum; Neumann boundary condition; mixed boundary conditions
UR - http://eudml.org/doc/252522
ER -
References
top- Amann H., Ordinary Differential Equations: An Introduction to the Nonlinear Analysis, Walter de Gruyter, Berlin, 1990. MR1071170
- Evans L.C., Partial Differencial Equations, American Mathematical Society, Providence, 1998. MR1625845
- Fučík S., Boundary value problems with jumping nonlinearities, Časopis pěst. mat. 101 (1976), 69–87. Zbl0332.34016MR0447688
- Massa E., Ruf B., On the Fučík spectrum for elliptic systems, Topol. Methods Nonlinear Anal. 27 (2006), 195–228. Zbl1132.35360MR2237452
- Massa E., Ruf B., 10.1016/j.jde.2006.11.021, J. Differential Equations 234 (2007), 311–336. Zbl1119.34015MR2298974DOI10.1016/j.jde.2006.11.021
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