Abstract
We study the second order nonlinear boundary value problems with non‐local integral conditions and construct the Fučík type spectrum for these problems.
Highlights
The Fučík equation x′′ = −μx+ + λx− (1.1)is a simple formally nonlinear equation with piece-wise linear right hand side
The Fučík spectrum for the problem (1.1), (1.2) is well known and consists of infinite set of curves which can be obtained analytically and graphically
The Fučík spectra for the Dirichlet and Neumann problems are similar, but the spectrum in the case of one of boundary conditions being in integral form differs essentially
Summary
Is a simple formally nonlinear equation with piece-wise linear right hand side. It was intensively investigated together with various boundary conditions ([6, 7, 10]), for instance, with the Dirichlet boundary conditions x(0) = 0, x(1) = 0. The Fučík spectra for the Dirichlet and Neumann problems are similar, but the spectrum in the case of one (or two) of boundary conditions being in integral form differs essentially. It was studied in the work of the author ([11]) and both analytical and graphical description was given in the case of boundary conditions x(0) = 0, x(s) ds = 0. The first one is the author’s work [11], where the spectrum of the equation (1.1) together with the integral condition (1.3) was considered and some properties of the spectrum were presented. We note that nonlocal boundary conditions (including integral conditions) are formulated for many applied problems, see e.g. [1, 2], where numerical algorithms for solution of such problems are proposed and investigated
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
