zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multiple solutions for a system of $(n_i p_i)$ boundary value problems. (English) Zbl 1160.34313
Summary: We consider the system of boundary value problems $$\cases u^{(n_i)}_i(t)+f_i(t,u_1(t),\dots,u_m(t))=0\\ u^{(j)}_i(0)=0,\quad u^{(p_i)}_i(1)=0\endcases$$ for $t\in[0,1]$, $i=1,\dots,m$ and $0\leq j\leq n_i-2$ where $n_i\geq 2$ and $1\leq p_i\leq n_i-1$. Several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs.

MSC:
34B15Nonlinear boundary value problems for ODE
WorldCat.org
Full Text: DOI EuDML
References:
[1] Agarwal, R. P.: Difference Equations and Inequalities. New York: Marcel Dekker 1992.
[2] Agarwal, R. P.: Focal Boundary Value Problems for Differential and Difference Equations. Dordrecht: Kluwer Acad. Publ. 1998. · Zbl 0914.34001
[3] Agarwal, R. P. and D. O’Regan: A coupled system of difference equations. Appl. Math. Comp. (to appear).
[4] Agarwal, R. P., O’Regan, D. and P. J. Y. Wong: Positive Solutions of Differential, Dif- ference and Integral Equations. Dordrecht: Kluwer Acad. Publ. 1999.
[5] Agarwal, R. P. and P. J. Y. Wong: Advanced Topics in Difference Equations. Dordrecht: Kluwer Acad. Publ. 1997. · Zbl 0878.39001
[6] Agarwal, R. P. and P. J. Y. Wong: Existence criteria for a system of two-point boundary value problems. Appl. Anal. (to appear). · Zbl 1031.34020 · doi:10.1080/00036810008840878
[7] Aronson, D., Crandall, M. G. and L. A. Peletier: Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlin. Anal. 6 (1982), 1001 - 1022. · Zbl 0518.35050 · doi:10.1016/0362-546X(82)90072-4
[8] Choi, Y. S. and G. S. Ludford: An unexpected stability result of the near-extinction dif- fusion flame for non-unity Lewis numbers. Q.J. Mech. Appl. Math. 42 (1989), 143 -158. · Zbl 0682.76076 · doi:10.1093/qjmam/42.1.143
[9] Cohen, D. C.: Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory. SIAM J. Appl. Math. 20 (1971), 1 - 13. P. J. Y Wong and R. P. Agarwal · Zbl 0219.34027 · doi:10.1137/0120001
[10] Dancer, E. N.: On the structure of solutions of an equation in catalysis theory when a parameter is large. J. Diff. Equ. 37 (1980), 404 - 437. · Zbl 0417.34042 · doi:10.1016/0022-0396(80)90107-2
[11] Eloe, P. W. and J. Henderson: Positive solutions for (n - 1, 1) conjugate boundary value problems. Nonlin. Anal. 28 (1997), 1669 - 1680. · Zbl 0871.34015 · doi:10.1016/0362-546X(95)00238-Q
[12] Eloe, P. W. and J. Henderson: Positive solutions and nonlinear multipoint conjugate eigenvalue problems. Electron. J. Diff. Equ. 3 (1997), 1 - 11. · Zbl 0888.34013 · emis:journals/EJDE/Volumes/1997/03/abstr.html · eudml:119392
[13] Eloe, P. W., Henderson, J. and E. R. Kaufmann: Multiple positive solutions for difference equations. J. Diff. Equ. Appl. 3 (1998), 219 - 229. · Zbl 1005.39502 · doi:10.1080/10236199808808098
[14] Fujita, H.: On the nonlinear equations \Delta u + eu = 0 and \partial v = \Delta v + ev. Bull. Amer. \partial t Math. Soc. 75 (1969), 132 - 135. · Zbl 0216.12101 · doi:10.1090/S0002-9904-1969-12175-0
[15] Gel’fand, I. M.: Some problems in the theory of quasilinear equations. Uspehi Mat. Nauka 14 (1959), 87 - 158; Engl. transl. in: Trans. Amer. Math. Soc. 29 (1963), 295 - 381.
[16] Henderson,J. and E. R. Kaufmann: Multiple positive solutions for focal boundary value problems. Comm. Appl. Anal. 1 (1997), 53 - 60. · Zbl 0887.34018
[17] Krasnosel’skii, M. A.: Positive Solutions of Operator Equations. Groningen: Noordhoff 1964. · Zbl 0121.10604
[18] Leggett, R. W. and L. R. Williams: A fixed point theorem with application to an infectious disease model. J. Math. Anal. Appl. 76 (1980), 91 - 97. · Zbl 0448.47044 · doi:10.1016/0022-247X(80)90062-1
[19] Parter, S.: Solutions of differential equations arising in chemical reactor processes. SIAM J. Appl. Math. 26 (1974), 687 - 716. · Zbl 0285.34013 · doi:10.1137/0126063
[20] Wong, P. J. Y.: Solutions of constant signs of a system of Sturm-Liouville boundary value problems. Mathl. Comp. Modelling 29 (1999), 27 - 38. · Zbl 1041.34015 · doi:10.1016/S0895-7177(99)00079-5
[21] Wong, P. J. Y.: A system of (ni, pi) boundary value problems with positive/nonpositive nonlinearities. J. Math. Anal. Appl. (to appear). · Zbl 0953.34013 · doi:10.1006/jmaa.1999.6671
[22] Wong, P. J. Y. and R. P. Agarwal: Fixed-sign solutions of a system of higher order difference equations. J. Comp. Appl. Math. 113 (2000), 167 - 181. · Zbl 0940.39003 · doi:10.1016/S0377-0427(99)00251-4
[23] Wong, P. J. Y. and R. P. Agarwal: Existence theorems for a system of difference equations with (n, p) type conditions (submitted). · Zbl 1025.39002 · doi:10.1016/S0096-3003(00)00078-3