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Keywords:
generalized multi-point boundary value problems; $p$-Laplace type operator; non-resonance; a priori estimates; topological degree
generalized multi-point boundary value problems; $p$-Laplace type operator; non-resonance; a priori estimates; topological degree
Summary:
This paper is devoted to the problem of existence of a solution for a non-resonant, non-linear generalized multi-point boundary value problem on the interval $[0,1]$. The existence of a solution is obtained using topological degree and some a priori estimates for functions satisfying the boundary conditions specified in the problem.
References:
[1] Cuan-zhi Bai, Jin-xuan Fang: Existence of multiple positive solutions for nonlinear $m$-point boundary-value problems. Appl. Math. Comput. 140 (2003), 297–305. DOI 10.1016/S0096-3003(02)00227-8 | MR 1953901
[2] A. V. Bitsadze: On the theory of nonlocal boundary value problems. Sov. Math. Dokl. 30 (1984), 8–10. MR 0757061 | Zbl 0586.30036
[3] A. V. Bitsadze: On a class of conditionally solvable nonlocal boundary value problems for harmonic functions. Sov. Math. Dokl. 31 (1985), 91–94. Zbl 0607.30039
[4] A. V. Bitsadze, A. A. Samarskiĭ: On some simple generalizations of linear elliptic boundary problems. Sov. Math. Dokl. 10 (1969), 398–400.
[5] W. Feng, J. R. L. Webb: Solvability of three point boundary value problems at resonance. Nonlinear Anal., Theory Methods Appl. 30 (1997), 3227–3238. DOI 10.1016/S0362-546X(96)00118-6 | MR 1603039
[6] W. Feng, J. R. L. Webb: Solvability of $m$-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212 (1997), 467–480. DOI 10.1006/jmaa.1997.5520 | MR 1464891
[7] M. Garcia-Huidobro, C. P. Gupta, and R. Manásevich: Solvability for a nonlinear three-point boundary value problem with $p$-Laplacian-like operator at resonance. Abstr. Appl. Anal. 6 (2001), 191–213. DOI 10.1155/S1085337501000550 | MR 1866004
[8] M. Garcia-Huidobro, C. P. Gupta, and R. Manásevich: An $m$-point boundary value problem of Neumann type for a $p$-Laplacian like operator. Nonlinear Anal., Theory Methods Appl. 56A (2004), 1071–1089. MR 2038737
[9] M. Garcia-Huidobro, C. P. Gupta, and R. Manásevich: A Dirichelet-Neumann $m$-point BVP with a $p$-Laplacian-like operator. Nonlinear Anal., Theory Methods Appl. 62 (2005), 1067–1089. DOI 10.1016/j.na.2005.04.020 | MR 2152998
[10] M. Garcia-Huidobro, R. Manásevich: A three point boundary value problem containing the operator $-(\phi (u^{\prime }))^{\prime } $. Discrete Contin. Dyn. Syst. Suppl. (2003), 313–319. MR 2018130
[11] C. P. Gupta: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. J. Math. Anal. Appl. 168 (1992), 540–551. DOI 10.1016/0022-247X(92)90179-H | MR 1176010 | Zbl 0763.34009
[12] C. P. Gupta: A note on a second order three-point boundary value problem. J. Math. Anal. Appl. 186 (1994), 277–281. DOI 10.1006/jmaa.1994.1299 | MR 1290657 | Zbl 0805.34017
[13] C. P. Gupta: A second order m-point boundary value problem at resonance. Nonlinear Anal., Theory Methods Appl. 24 (1995), 1483–1489. DOI 10.1016/0362-546X(94)00204-U | MR 1327929 | Zbl 0839.34027
[14] C. P. Gupta: Existence theorems for a second order $m$-point boundary value problem at resonance. Int. J. Math. Math. Sci. 18 (1995), 705–710. DOI 10.1155/S0161171295000901 | MR 1347059 | Zbl 0839.34027
[15] C. P. Gupta: Solvability of a multi-point boundary value problem at resonance. Result. Math. 28 (1995), 270–276. DOI 10.1007/BF03322257 | MR 1356893 | Zbl 0843.34023
[16] C. P. Gupta: A generalized multi-point boundary value problem for second order ordinary differential equations. Appl. Math. Comput. 89 (1998), 133–146. DOI 10.1016/S0096-3003(97)81653-0 | MR 1491699 | Zbl 0910.34032
[17] C. P. Gupta, S. K. Ntouyas, and P. Ch. Tsamatos: On an $m$-point boundary value problem for second order ordinary differential equations. Nonlinear Anal., Theory Methods Appl. 23 (1994), 1427–1436. DOI 10.1016/0362-546X(94)90137-6 | MR 1306681
[18] C. P. Gupta, S. Ntouyas, and P. Ch. Tsamatos: Solvability of an $m$-point boundary value problem for second order ordinary differential equations. J. Math. Anal. Appl. 189 (1995), 575–584. DOI 10.1006/jmaa.1995.1036 | MR 1312062
[19] C. P. Gupta, S. K. Ntouyas, and P. Ch. Tsamatos: Existence results for $m$-point boundary value problems. Differ. Equ. Dyn. Syst. 2 (1994), 289–298. MR 1386275
[20] C. P. Gupta, S. K. Ntouyas, and P. Ch. Tsamatos: On the solvability of some multi-point boundary value problems. Appl. Math. 41 (1996), 1–17. MR 1365136
[21] C. P. Gupta, S. K. Ntouyas, and P. Ch. Tsamatos: Existence results for multi-point boundary value problems for second order ordinary differential equations. Bull. Greek Math. Soc. 43 (2000), 105–123. MR 1846952
[22] C. P. Gupta, S. Trofimchuk: Solvability of a multi-point boundary value problem of Neumann type. Abstr. Appl. Anal. 4 (1999), 71–81. DOI 10.1155/S1085337599000093 | MR 1810319
[23] V. A. Il’in, E. I. Moiseev: Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and difference aspects. Differ. Equ. 23 (1987), 803–810.
[24] V. A. Il’in, E. I. Moiseev: Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator. Differ. Equ. 23 (1987), 979–987.
[25] B. Liu: Solvability of multi-point boundary value problem at resonance. IV. Appl. Math. Comput. 143 (2003), 275–299. DOI 10.1016/S0096-3003(02)00361-2 | MR 1981696 | Zbl 1071.34014
[26] Y. Liu, W. Ge: Multiple positive solutions to a three-point boundary value problem with $p$-Laplacian. J. Math. Anal. Appl. 277 (2003), 293–302. DOI 10.1016/S0022-247X(02)00557-7 | MR 1954477 | Zbl 1026.34028
[27] N. G. Lloyd: Degree Theory. Cambridge University Press, Cambridge, 1978. MR 0493564 | Zbl 0367.47001
[28] J. Mawhin: Topological degree methods in nonlinear boundary value problems. In: NSF-CBMS Regional Conference Series in Math. No. 40, Americal Mathematical Society, Providence, 1979. MR 0525202 | Zbl 0414.34025
[29] J. Mawhin: A simple approach to Brouwer degree based on differential forms. Adv. Nonlinear Stud. 4 (2004), 501–514. DOI 10.1515/ans-2004-0409 | MR 2100911 | Zbl 1082.47052
[30] S. Sedziwy: Multipoint boundary value problems for a second order differential equations. J. Math. Anal. Appl. 236 (1999), 384–398. DOI 10.1006/jmaa.1999.6441 | MR 1704590
[31] H. B. Thompson, C. Tisdell: Three-point boundary value problems for second-order ordinary differential equations. Math. Comput. Modelling 34 (2001), 311–318. DOI 10.1016/S0895-7177(01)00063-2 | MR 1835829
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