ON A FUCIK TYPE SPECTRAL PROBLEM FOR THE SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH THE INTEGRAL BOUNDARY CONDITION

F. SADYRBAEV; N. SERGEJEVA

Title	ON A FUCIK TYPE SPECTRAL PROBLEM FOR THE SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH THE INTEGRAL BOUNDARY CONDITION
Publication Type	Journal Article
Year of Publication	2011
Authors	SADYRBAEV, F, SERGEJEVA, N
Volume	15
Issue	4
Start Page	557
Pagination	11
Date Published	2011
ISSN	1083-2564
AMS	34B15
Abstract	In this article we consider the equation ${\ x'' = -\mu f(x^+)+\lambda g(x^-) }$, where ${\ x^+ = \text{max}\{\ x,0 \}\ , x^-=\text{max}\{ \ -x,0\} }$ together with the boundary conditions ${\ x(0)=0, x(b)=\gamma \int_0^b x(s)\, ds }$. We give description of a set of (µ, λ) such that the problem has a nontrivial solution.
URL	http://www.acadsol.eu/en/articles/15/4/11.pdf
Refereed Designation	Refereed
Full Text	REFERENCES [1] Z. Buike. Differentiation and integration of the lemniscate functions. Daugavpils University, Dept. Math., Research for Bachelor degree, 2005, 1–36 (in Latvian). [2] S. Fuˇc´ık. Boundary value problems with jumping nonlinearities, Casopis pro pˇeˇst. mat. ˇ , 101,p. 69, 1976. [3] A. Gritsans and F. Sadyrbaev. Remarks on lemniscatic functions. Acta Univ. Latviensis, Ser. Mathematics, vol. 688 (2005), 39–50. [4] A. Gritsans and F. Sadyrbaev. Nonlinear Spectra for Parameter Dependent Ordinary Differential Equations. Nonlinear Analysis: Modelling and Control, 2007 (12), No. 2, 253–267. [5] A. Gritsans and F. Sadyrbaev. On nonlinear Fuˇc´ık type spectra. Math. Modelling and Analysis,V.13 (2008), N.2, 203–210. [6] P. Korman and Y. Li. Generalized Averages for Solutions of Two-Point Dirichlet Problems,J. Math. Anal. Appl., 239, p. 478, 1999. [7] A. Kufner and S. Fuˇc´ık. Nonlinear Differential Equations, Nauka, Moscow, 1988 (Russian translation of: Kufner A., Fuˇcik S. Nonlinear Differential Equations, Elsevier, AmsterdamOxford-NewYork, 1980). [8] F. Sadyrbaev. Multiplicity in Parameter-Dependent Problems for Ordinary Differential Equations. Math. Modelling and Analysis, V.14 (2009), N.4, 503–514. [9] R. Schaaf. Global Solution Branches of Two Point Boundary Value Problems, Lecture Notes in Mathematics, 1458, Springer-Verlag, 1990. [10] N. Sergejeva. On the unusual Fuˇc´ık spectrum, Discrete and Continuous Dynamical Systems, Supplement Volume 2007. Dedicated to the 6th AIMS Conference, Poitiers, France (2007),920–926. [11] N. Sergejeva. On nonlinear spectra for some nonlocal boundary value problems. Math. Modelling and Analysis, 13 (2008), 1, 87–98 [12] N. Sergejeva. On some problems with nonlocal integral condition. Math. Modelling and Analysis,15 (2010), 1, 113–126 [13] E. T. Whittaker and G.N. Watson. A Course of Modern Analysis, Part II. Cambridge Univ.Press, 1927.