Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
fixed point index; cone; nontrivial solution
fixed point index; cone; nontrivial solution
Summary:
References:
[1] Agarwal R.P., Avery R., Henderson J., O'Regan D.: The five functionals fixed point theorem generalized to multivalued maps. J. Nonlinear Convex Anal. 4 (2003), 455--462. MR 2026456 | Zbl 1065.47050
[2] Agarwal R.P., O'Regan D.: A note on the existence of multiple fixed points for multivalued maps with applications. J. Differential Equations 160 (2000), 389--403. MR 1736998 | Zbl 1008.47055
[3] Agarwal R.P., O'Regan D.: A generalization of the Petryshyn-Leggett-Williams fixed point theorem with applications to integral inclusions. Appl. Math. Comput. 123 (2001), 263--274. MR 1847915 | Zbl 1033.47037
[4] Amann H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976), 620--709. MR 0415432 | Zbl 0345.47044
[5] Andres J., Górniewicz L.: Topological Fixed Point Principles for Boundary Value Problems. Kluwer Academic Publishers, Dordrecht, 2003. MR 1998968
[6] Aubin J.P., Cellina A.: Differential Inclusions. Springer, Berlin, 1984. MR 0755330 | Zbl 0538.34007
[7] Benchohra M., Ntouyas S.K.: A note on a three point boundary value problem for second order differental inclusions. Math. Notes (Miskolc) 2 (2001), 39--47. MR 1854436
[8] Benchohra M., Ouahab A.: Upper and lower solutions method for differential inclusions with integral boundary conditions. J. Appl. Math. Stoch. Anal. 2006, Art. ID 10490, 10 pp. MR 2212591 | Zbl 1122.34006
[9] Dhage B.C., Graef J.R.: On boundary-value problems for second order perturbed differential inclusions. Appl. Anal. 84 (2005), 953--970. MR 2172410 | Zbl 1088.34009
[10] Dhage B.C., Ntouyas S.K., Cho Y.J.: On the second order discontinuous differential inclusions. J. Appl. Funct. Anal. 1 (2006), 469--476. MR 2220805 | Zbl 1108.34302
[11] Deimling K.: Nonlinear Functional Analysis. Springer, Berlin, 1985. MR 0787404 | Zbl 0559.47040
[12] Deimling K.: Multivalued Differential Equations. Walter de Gruyter, Berlin, 1992. MR 1189795 | Zbl 0820.34009
[13] Erbe L., Ma R., Tisdell C.C.: On two point boundary value problems for second order differential inclusions. Dynam. Systems Appl. 15 (2006), 79--88. MR 2194094 | Zbl 1112.34008
[14] Fitzpatrick P.M., Petryshyn W.V.: Fixed point theorems and the fixed point index for multivalued mappings in cones. J. London Math. Soc. 12 (1975/76), 75--85. MR 0405180 | Zbl 0329.47022
[15] Franco D., Infante G., O'Regan D.: Positive and nontrivial solutions for the Urysohn integral equation. Acta Math. Sin. (Engl. Ser.) 22 (2006), 1745--1750. MR 2262433 | Zbl 1130.45004
[16] Franco D., Infante G., O'Regan D.: Nontrivial solutions in abstract cones for Hammerstein integral systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 14 (2007), 837--850. MR 2369916 | Zbl 1139.45004
[17] Guo D., Lakshmikantham V.: Nonlinear Problems in Abstract Cones. Academic Press, Boston, 1988. MR 0959889 | Zbl 0661.47045
[18] Hong S., Wang L.: Existence of solutions for integral inclusions. J. Math. Anal. Appl. 317 (2006), 429--441. MR 2208929 | Zbl 1125.45006
[19] Hong S.: Multiple positive solutions for a class of integral inclusions. J. Comput. Appl. Math. 214 (2008), 19--29. MR 2391669 | Zbl 1151.45004
[20] Infante G.: Eigenvalues of some non-local boundary-value problems. Proc. Edinb. Math. Soc. 46 (2003), 75--86. MR 1961173 | Zbl 1049.34015
[21] Infante G.: Nonzero solutions of second order problems subject to nonlinear BCs. Dynamic systems and applications. Vol. 5, Dynamic, Atlanta, GA, (2008), 222--226. MR 2468144
[22] Infante G., Webb J.R.L.: Nonzero solutions of Hammerstein integral equations with discontinuous kernels. J. Math. Anal. Appl. 272 (2002), 30--42. MR 1930701 | Zbl 1008.45004
[23] Infante G., Webb J.R.L.: Three point boundary value problems with solutions that change sign. J. Integral Equations Appl. 15 (2003), 37--57. MR 2004793 | Zbl 1055.34023
[24] Infante G., Webb J.R.L.: Nonlinear nonlocal boundary value problems and perturbed Hammerstein integral equations. Proc. Edinb. Math. Soc. 49 (2006), 637--656. MR 2266153
[25] Infante G., Webb J.R.L.: Loss of positivity in a nonlinear scalar heat equation. NoDEA Nonlinear Differential Equations Appl. 13 (2006), 249--261. MR 2243714 | Zbl 1112.34017
[26] Karakostas G.L., Tsamatos P.Ch.: Existence of multiple positive solutions for a nonlocal boundary value problem. Topol. Methods Nonlinear Anal. 19 (2002), 109--121. MR 1921888 | Zbl 1071.34023
[27] Krasnosel'skiĭ M.A., Zabreĭko P.P.: Geometrical Methods of Nonlinear Analysis. Springer, Berlin, 1984. MR 0736839
[28] Lan K.Q.: Multiple positive solutions of Hammerstein integral equations with singularities. Diff. Eqns and Dynam. Syst. 8 (2000), 175--195. MR 1862603 | Zbl 0977.45001
[29] Lan K.Q.: Multiple positive solutions of semilinear differential equations with singularities. J. London Math. Soc. 63 (2001), 690--704. MR 1825983 | Zbl 1032.34019
[30] Lan K.Q.: Positive characteristic values and optimal constants for three-point boundary value problems. Differential & Difference Equations and Applications, 623--633, Hindawi Publ. Corp., New York, 2006. MR 2309394 | Zbl 1129.34008
[31] Lan K.Q.: Properties of kernels and multiple positive solutions for three-point boundary value problems. Appl. Math. Lett. 20 (2007), 352--357. MR 2292572 | Zbl 1125.34307
[32] Lan K.Q., Yang G.C.: Optimal constants for two point boundary value problems. Discrete Contin. Dyn. Syst., suppl. (2007), 624--633. MR 2409898 | Zbl 1163.34328
[33] Lasota A., Opial Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 781--786. MR 0196178 | Zbl 0151.10703
[34] Ma T.: Topological degrees of set-valued compact fields in locally convex spaces. Dissertationes Math. (Rozprawy Mat.) 92 (1972), 1--42. MR 0309103 | Zbl 0211.25903
[35] Ma R., Castaneda N.: Existence of solutions of nonlinear $m$-point boundary value problems. J. Math. Anal. Appl. 256 (2001), 556--567. MR 1821757 | Zbl 0988.34009
[36] Marino G.: Nonlinear boundary value problems for multivalued differential equations in Banach spaces. Nonlinear Anal. 14 (1990), 545--558. MR 1044285 | Zbl 0692.34018
[37] O'Regan D.: Integral inclusions of upper semi-continuous or lower semi-continuous type. Proc. Amer. Math. Soc. 124 (1996), 2391--2399. MR 1342037 | Zbl 0860.45007
[38] O'Regan D., Zima M.: Leggett-Williams norm-type fixed point theorems for multivalued mappings. Appl. Math. Comput. 187 (2007), 1238-1249. MR 2321327 | Zbl 1126.47046
[39] O'Regan D., Zima M.: Leggett-Williams theorems for coincidences of multivalued operators. Nonlinear Anal. 68 (2008), 2879--2888. MR 2404806 | Zbl 1152.47041
[40] Webb J.R.L.: Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Anal. 47 (2001), 4319--4332. MR 1975828 | Zbl 1042.34527
[41] Webb J.R.L.: Multiple positive solutions of some nonlinear heat flow problems. Discrete Contin. Dyn. Syst., suppl. (2005), 895--903. MR 2192752 | Zbl 1161.34007
[42] Webb J.R.L.: Optimal constants in a nonlocal boundary value problem. Nonlinear Anal. 63 (2005), 672--685. MR 2188140 | Zbl 1153.34320
[43] Webb J.R.L.: Fixed point index and its application to positive solutions of nonlocal boundary value problems. Seminar of Mathematical Analysis, Univ. Sevilla Secr. Publ., Seville, 2006, pp. 181--205. MR 2276962 | Zbl 1124.47040
Search
Partner of
