| Title:
|
Nonlocal systems of BVPs with asymptotically superlinear boundary conditions (English) |
| Author:
|
Goodrich, Christopher S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
79-97 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel measures. We conclude with a numerical example to illustrate the use of one of our two main results. (English) |
| Keyword:
|
coupled system of second-order boundary value problems |
| Keyword:
|
nonlocal boundary condition |
| Keyword:
|
nonlinear boundary condition |
| Keyword:
|
superlinear growth |
| Keyword:
|
positive solution |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| MSC:
|
47H07 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1249.34054 |
| idMR:
|
MR2880912 |
| . |
| Date available:
|
2012-02-07T10:25:37Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141827 |
| . |
| Reference:
|
[1] Agarwal R., Meehan M., O'Regan D.: Fixed Point Theory and Applications.Cambridge University Press, Cambridge, 2001. Zbl 1159.54001, MR 1825411 |
| Reference:
|
[2] Dunninger D., Wang H.: Existence and multiplicity of positive solutions for elliptic systems.Nonlinear Anal. 29 (1997), 1051–1060. Zbl 0885.35028, MR 1460438, 10.1016/S0362-546X(96)00092-2 |
| Reference:
|
[3] Goodrich C.S.: Positive solutions to boundary value problems with nonlinear boundary conditions.Nonlinear Anal. 75 (2012), 417–432. MR 2846811, 10.1016/j.na.2011.08.044 |
| Reference:
|
[4] Goodrich C.S.: On nonlocal BVPs with boundary conditions with asymptotically sublinear or superlinear growth.Math. Nachr.(to appear). |
| Reference:
|
[5] Graef J., Webb J.R.L.: Third order boundary value problems with nonlocal boundary conditions.Nonlinear Anal. 71 (2009), 1542–1551. Zbl 1189.34034, MR 2524369, 10.1016/j.na.2008.12.047 |
| Reference:
|
[6] Infante G.: Nonlocal boundary value problems with two nonlinear boundary conditions.Commun. Appl. Anal. 12 (2008), 279–288. Zbl 1198.34025, MR 2499284 |
| Reference:
|
[7] Infante G., Pietramala P.: Existence and multiplicity of non-negative solutions for systems of perturbed Hammerstein integral equations.Nonlinear Anal. 71 (2009), 1301–1310. Zbl 1169.45001, MR 2527550, 10.1016/j.na.2008.11.095 |
| Reference:
|
[8] Infante G., Pietramala P.: Eigenvalues and non-negative solutions of a system with nonlocal BCs.Nonlinear Stud. 16 (2009), 187–196. Zbl 1184.34027, MR 2527180 |
| Reference:
|
[9] Infante G., Pietramala P.: A third order boundary value problem subject to nonlinear boundary conditions.Math. Bohem. 135 (2010), 113–121. Zbl 1224.34036, MR 2723078 |
| Reference:
|
[10] Kang P., Wei Z.: Three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations.Nonlinear Anal. 70 (2009), 444–451. Zbl 1169.34014, MR 2468250, 10.1016/j.na.2007.12.014 |
| Reference:
|
[11] Kelley W.G., Peterson A.C.: The Theory of Differential Equations: Classical and Qualitative.Prentice Hall, Upper Saddle River, 2004. Zbl 1201.34001, MR 2640364 |
| Reference:
|
[12] Webb J.R.L., Infante G.: Positive solutions of nonlocal boundary value problems: a unified approach.J. Lond. Math. Soc. (2) 74 (2006), 673–693. Zbl 1115.34028, MR 2286439, 10.1112/S0024610706023179 |
| Reference:
|
[13] Webb J.R.L.: Nonlocal conjugate type boundary value problems of higher order.Nonlinear Anal. 71 (2009), 1933–1940. Zbl 1181.34025, MR 2524407, 10.1016/j.na.2009.01.033 |
| Reference:
|
[14] Webb J.R.L.: Solutions of nonlinear equations in cones and positive linear operators.J. Lond. Math. Soc. (2) 82 (2010), 420–436. Zbl 1209.47017, MR 2725047, 10.1112/jlms/jdq037 |
| Reference:
|
[15] Webb J.R.L.: Remarks on a non-local boundary value problem.Nonlinear Anal. 72 (2010), 1075–1077. Zbl 1186.34029, MR 2579370, 10.1016/j.na.2009.07.047 |
| Reference:
|
[16] Yang Z.: Positive solutions to a system of second-order nonlocal boundary value problems.Nonlinear Anal. 62 (2005), 1251–1265. Zbl 1089.34022, MR 2154107, 10.1016/j.na.2005.04.030 |
| Reference:
|
[17] Yang Z.: Positive solutions of a second-order integral boundary value problem.J. Math. Anal. Appl. 321 (2006), 751–765. Zbl 1106.34014, MR 2241153, 10.1016/j.jmaa.2005.09.002 |
| . |
