zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions. (English) Zbl 1221.34062

The author studies the existence of symmetric positive solutions for the nonlinear nonlocal boundary problem

(g(t)x ' (t)) ' +w(t)f(t,x(t))=0,
ax(0)-blim t0 + g(t)x ' (t)= 0 1 h(s)x(s)ds,ax(1)+blim t1 - g(t)x ' (t)= 0 1 h(s)x(s)ds,

where a,b>0, gC 1 ([0,1],(0,)), wL p (0,1) and hL 1 ((0,1),(0,)) are symmetric on [0,1], respectively; f:[0,1]×[0,)[0,) is continuous and f(t,x)=f(1-t,x). The main tool is the theory of fixed point index.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
[1]Csavinszky, P.: Universal approximate solution of the Thomas–Fermi equation for ions, Phys. rev. A. 8, 1688-1701 (1973)
[2]Granas, A.; Guenther, R. B.; Lee, J. W.: Nonlinear boundary value problems for ordinary differential equations, Dissertationes math. (1985) · Zbl 0615.34010
[3]Granas, A.; Guenther, R. B.; Lee, J. W.: A note on the Thomas–Fermi equations, Z. angew. Math. mech. 61, 240-241 (1981)
[4]Luning, C. D.; Perry, W. L.: Positive solutions of negative exponent generalized Emden–Fowler boundary value problems, SIAM J. Math. anal. 12, 874-879 (1981) · Zbl 0478.34021 · doi:10.1137/0512073
[5]Wong, J. S. W.: On the generalized Emden–Fowler equations, SIAM rev. 17, 339-360 (1975) · Zbl 0295.34026 · doi:10.1137/1017036
[6]Lan, K.; Webb, J. R. L.: Positive solutions of semilinear differential equations with singularities, J. differential equations 148, 407-421 (1998) · Zbl 0909.34013 · doi:10.1006/jdeq.1998.3475
[7]Liu, L.; Sun, Y.: Positive solutions of singular boundary value problems of differential equations, Acta math. Sci. 25A, No. 4, 554-563 (2005) · Zbl 1110.34308
[8]Webb, J. R. L.: Positive solutions of some three point boundary value problems via fixed point index theory, Nonlinear anal. 47, 4319-4332 (2001) · Zbl 1042.34527 · doi:10.1016/S0362-546X(01)00547-8
[9]Yao, Q.: Existence and iteration of n symmetric positive solutions for a singular two-point boundary value problem, Comput. math. Appl. 47, 1195-1200 (2004) · Zbl 1062.34024 · doi:10.1016/S0898-1221(04)90113-7
[10]Henderson, J.; Thompson, H. B.: Multiple symmetric positive solutions for a second order boundary value problem, Proc. amer. Math. soc. 128, 2373-2379 (2000) · Zbl 0949.34016 · doi:10.1090/S0002-9939-00-05644-6
[11]Li, F.; Zhang, Y.: Multiple symmetric nonnegative solutions of second-order ordinary differential equations, Appl. math. Lett. 17, 261-267 (2004) · Zbl 1060.34009 · doi:10.1016/S0893-9659(04)90061-4
[12]Avery, R. I.; Henderson, J.: Three symmetric positive solutions for a second-order boundary value problem, Appl. math. Lett. 13, 1-7 (2000) · Zbl 0961.34014 · doi:10.1016/S0893-9659(99)00177-9
[13]Kosmatov, N.: Symmetric solutions of a multi-point boundary value problem, J. math. Anal. appl. 309, 25-36 (2005) · Zbl 1085.34011 · doi:10.1016/j.jmaa.2004.11.008
[14]Sun, Y.: Optimal existence criteria for symmetric positive solutions to a three-point boundary value problem, Nonlinear anal. 66, 1051-1063 (2007) · Zbl 1114.34022 · doi:10.1016/j.na.2006.01.004
[15]Cannon, J. R.: The solution of the heat equation subject to the specification of energy, Quart. appl. Math. 21, No. 2, 155-160 (1963) · Zbl 0173.38404
[16]Ionkin, N. I.: Solution of a boundary value problem in heat conduction theory with nonlocal boundary conditions, Differential equations 13, 294-304 (1977)
[17]Chegis, R. Yu.: Numerical solution of a heat conduction problem with an integral boundary condition, Litovsk. mat. Sb. 24, 209-215 (1984) · Zbl 0578.65092
[18]Boucherif, A.: Second-order boundary value problems with integral boundary conditions, Nonlinear anal. 70, 364-371 (2009) · Zbl 1169.34310 · doi:10.1016/j.na.2007.12.007
[19]Infante, G.: Eigenvalues and positive solutions of odes involving integral boundary conditions, Discrete contin. Dyn. syst., No. Suppl., 436-442 (2005) · Zbl 1169.34311
[20]Yang, Z.: Positive solutions of a second order integral boundary value problem, J. math. Anal. appl. 321, 751-765 (2006) · Zbl 1106.34014 · doi:10.1016/j.jmaa.2005.09.002
[21]Ahmad, B.; Alsaedi, A.; Alghamdi, B. S.: Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear anal. RWA 9, 1727-1740 (2008) · Zbl 1154.34311 · doi:10.1016/j.nonrwa.2007.05.005
[22]Ahmad, B.; Alsaedi, A.: Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions, Nonlinear anal. RWA 10, 358-367 (2009) · Zbl 1154.34314 · doi:10.1016/j.nonrwa.2007.09.004
[23]Feng, M.; Du, B.; Ge, W.: Impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian, Nonlinear anal. 70, 3119-3126 (2009) · Zbl 1169.34022 · doi:10.1016/j.na.2008.04.015
[24]Feng, M.; Zhang, X.; Ge, W.: New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions, Bound. value probl. 2011 (2011)
[25]Li, Y.; Zhang, T.: Multiple positive solutions of fourth-order impulsive differential equations with integral boundary conditions and one-dimensional p-Laplacian, Bound. value probl. 2011 (2011) · Zbl 1206.47096 · doi:10.1155/2011/654871
[26]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)