Geodesic
A third order boundary value problem subject to nonlinear boundary conditions
Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 113-121

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MR Zbl
Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
DOI : 10.21136/MB.2010.140687
Classification : 34B10, 34B18, 47H10, 47H30
Keywords: positive solution; nonlinear boundary conditions; third order problem; cone; fixed point index 
Infante, Gennaro; Pietramala, Paolamaria. A third order boundary value problem subject to nonlinear boundary conditions. Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 113-121. doi: 10.21136/MB.2010.140687
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[1] Anderson, D. R., Davis, J. M.: Multiple solutions and eigenvalues for third-order right focal boundary value problems. J. Math. Anal. Appl. 267 (2002), 135-157. | DOI | MR | Zbl

[2] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976), 620-709. | DOI | MR | Zbl

[3] Cabada, A., Minhós, F., Santos, A. I.: Solvability for a third order fully discontinuous equation with nonlinear functional boundary conditions. J. Math. Anal. Appl. 322 (2006), 735-748. | DOI | MR

[4] Clark, S., Henderson, J.: Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations. Proc. Amer. Math. Soc. 134 (2006), 3363-3372. | DOI | MR | Zbl

[5] Franco, D., O'Regan, D.: Existence of solutions to second order problems with nonlinear boundary conditions. Discrete Contin. Dyn. Syst. suppl. (2005), 273-280. | MR

[6] Graef, J. R., Webb, J. R. L.: Third order boundary value problems with nonlocal boundary conditions. Nonlinear Anal. 71 (2009), 1542-1551. | MR | Zbl

[7] Graef, J. R., Yang, B.: Positive solutions of a third order nonlocal boundary value problem. Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 89-97. | MR | Zbl

[8] Graef, J. R., Henderson, J., Yang, B.: Existence and nonexistence of positive solutions of an $n$-th order nonlocal boundary value problem. Proc. Dynam. Systems Appl. 5 (2008), 186-191. | MR | Zbl

[9] Guidotti, P., Merino, S.: Gradual loss of positivity and hidden invariant cones in a scalar heat equation. Differ. Int. Equations 13 (2000), 1551-1568. | MR | Zbl

[10] Guo, D., Lakshmikantham, V.: Nonlinear problems in abstract cones. Academic Press, Boston (1988). | MR | Zbl

[11] Infante, G.: Positive solutions of some nonlinear BVPs involving singularities and integral BCs. Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 99-106. | DOI | MR

[12] Infante, G.: Positive solutions of differential equations with nonlinear boundary conditions. Discrete Contin. Dyn. Syst. suppl. (2003), 432-438. | MR | Zbl

[13] Infante, G.: Nonzero solutions of second order problems subject to nonlinear BCs. Dynamic systems and applications. Vol. 5, 222-226, Dynamic, Atlanta, GA (2008). | MR | Zbl

[14] Infante, G.: Nonlocal boundary value problems with two nonlinear boundary conditions. Commun. Appl. Anal. 12 (2008), 279-288. | MR | Zbl

[15] Infante, G., Pietramala, P.: Existence and multiplicity of non-negative solutions for systems of perturbed Hammerstein integral equations. Nonlinear Anal. 71 (2009), 1301-1310. | DOI | MR | Zbl

[16] Infante, G., Pietramala, P.: A cantilever equation with nonlinear boundary conditions. Electron. J. Qual. Theory Differ. Equ., Special Edition I (2009), 14 pp. | MR | Zbl

[17] Infante, G., Webb, J. R. L.: Loss of positivity in a nonlinear scalar heat equation. NoDEA, Nonlinear Differential Equations Appl. 13 (2006), 249-261. | DOI | MR | Zbl

[18] Infante, G., Webb, J. R. L.: Nonlinear nonlocal boundary value problems and perturbed Hammerstein integral equations. Proc. Edinb. Math. Soc. 49 (2006), 637-656. | DOI | MR

[19] Kong, L., Wang, J.: Multiple positive solutions for the one-dimensional $p$-Laplacian. Nonlinear Anal. 42 (2000), 1327-1333. | DOI | MR | Zbl

[20] Krasnosel'skiǐ, M. A., Zabreǐko, P. P.: Geometrical Methods of Nonlinear Analysis. Springer, Berlin (1984). | MR

[21] Lan, K. Q.: Multiple positive solutions of semilinear differential equations with singularities. J. London Math. Soc. 63 (2001), 690-704. | DOI | MR | Zbl

[22] Minhós, F. M.: On some third order nonlinear boundary value problems: existence, location and multiplicity results. J. Math. Anal. Appl. 339 (2008), 1342-1353. | DOI | MR | Zbl

[23] Palamides, P. K., Infante, G., Pietramala, P.: Nontrivial solutions of a nonlinear heat flow problem via Sperner's Lemma. Appl. Math. Lett. 22 (2009), 1444-1450. | DOI | MR | Zbl

[24] Palamides, P. K., Palamides, A. P.: A third-order 3-point BVP. Applying Krasnosel'skiǐ's theorem on the plane without a Green's function. Electron. J. Qual. Theory Differ. Equ. (2008), 15 pp. | MR

[25] Palamides, A. P., Smyrlis, G.: Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green's function. Nonlinear Anal. 68 (2008), 2104-2118. | MR | Zbl

[26] Wang, Y., Ge, W.: Existence of solutions for a third order differential equation with integral boundary conditions. Comput. Math. Appl. 53 (2007), 144-154. | DOI | MR | Zbl

[27] Webb, J. R. L.: Multiple positive solutions of some nonlinear heat flow problems. Discrete Contin. Dyn. Syst. suppl. (2005), 895-903. | MR | Zbl

[28] Webb, J. R. L.: Optimal constants in a nonlocal boundary value problem. Nonlinear Anal. 63 (2005), 672-685. | DOI | MR | Zbl

[29] Webb, J. R. L., Infante, G.: Positive solutions of nonlocal boundary value problems: a unified approach. J. London Math. Soc. 74 (2006), 673-693. | DOI | MR | Zbl

[30] Webb, J. R. L., Lan, K. Q.: Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal. 27 (2006), 91-116. | MR | Zbl

[31] Yang, B.: Positive solutions of a third-order three-point boundary-value problem. Electron. J. Differ. Equations (2008), 10 pp. | MR | Zbl

[32] Yang, Z.: Positive solutions of a second-order integral boundary value problem. J. Math. Anal. Appl. 321 (2006), 751-765. | DOI | MR | Zbl

[33] Yao, Q.: Positive solutions of singular third-order three-point boundary value problems. J. Math. Anal. Appl. 354 (2009), 207-212. | DOI | MR | Zbl

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