A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a p -Laplacian type operator

Chaitan P. Gupta

Applications of Mathematics (2007)

  • Volume: 52, Issue: 5, page 417-430
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Gupta, Chaitan P.. "A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a $p$-Laplacian type operator." Applications of Mathematics 52.5 (2007): 417-430. <http://eudml.org/doc/33299>.

@article{Gupta2007,
abstract = {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.},
author = {Gupta, Chaitan P.},
journal = {Applications of Mathematics},
keywords = {generalized multi-point boundary value problems; $p$-Laplace type operator; non-resonance; a priori estimates; topological degree; generalized multi-point boundary value problems; -Laplace type operator},
language = {eng},
number = {5},
pages = {417-430},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a $p$-Laplacian type operator},
url = {http://eudml.org/doc/33299},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Gupta, Chaitan P.
TI - A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a $p$-Laplacian type operator
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 5
SP - 417
EP - 430
AB - 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.
LA - eng
KW - generalized multi-point boundary value problems; $p$-Laplace type operator; non-resonance; a priori estimates; topological degree; generalized multi-point boundary value problems; -Laplace type operator
UR - http://eudml.org/doc/33299
ER -

References

top
  1. 10.1016/S0096-3003(02)00227-8, Appl. Math. Comput. 140 (2003), 297–305. (2003) MR1953901DOI10.1016/S0096-3003(02)00227-8
  2. On the theory of nonlocal boundary value problems, Sov. Math. Dokl. 30 (1984), 8–10. (1984) Zbl0586.30036MR0757061
  3. On a class of conditionally solvable nonlocal boundary value problems for harmonic functions, Sov. Math. Dokl. 31 (1985), 91–94. (1985) Zbl0607.30039
  4. On some simple generalizations of linear elliptic boundary problems, Sov. Math. Dokl. 10 (1969), 398–400. (1969) 
  5. 10.1016/S0362-546X(96)00118-6, Nonlinear Anal., Theory Methods Appl. 30 (1997), 3227–3238. (1997) MR1603039DOI10.1016/S0362-546X(96)00118-6
  6. 10.1006/jmaa.1997.5520, J.  Math. Anal. Appl. 212 (1997), 467–480. (1997) MR1464891DOI10.1006/jmaa.1997.5520
  7. 10.1155/S1085337501000550, Abstr. Appl. Anal. 6 (2001), 191–213. (2001) MR1866004DOI10.1155/S1085337501000550
  8. An m -point boundary value problem of Neumann type for a p -Laplacian like operator, Nonlinear Anal., Theory Methods Appl. 56A (2004), 1071–1089. (2004) MR2038737
  9. 10.1016/j.na.2005.04.020, Nonlinear Anal., Theory Methods Appl. 62 (2005), 1067–1089. (2005) MR2152998DOI10.1016/j.na.2005.04.020
  10. A three point boundary value problem containing the operator - ( φ ( u ' ) ) ' , Discrete Contin. Dyn. Syst. Suppl. (2003), 313–319. (2003) MR2018130
  11. 10.1016/0022-247X(92)90179-H, J.  Math. Anal. Appl. 168 (1992), 540–551. (1992) Zbl0763.34009MR1176010DOI10.1016/0022-247X(92)90179-H
  12. 10.1006/jmaa.1994.1299, J.  Math. Anal. Appl. 186 (1994), 277–281. (1994) Zbl0805.34017MR1290657DOI10.1006/jmaa.1994.1299
  13. 10.1016/0362-546X(94)00204-U, Nonlinear Anal., Theory Methods Appl. 24 (1995), 1483–1489. (1995) Zbl0839.34027MR1327929DOI10.1016/0362-546X(94)00204-U
  14. 10.1155/S0161171295000901, Int. J.  Math. Math. Sci. 18 (1995), 705–710. (1995) Zbl0839.34027MR1347059DOI10.1155/S0161171295000901
  15. 10.1007/BF03322257, Result. Math. 28 (1995), 270–276. (1995) Zbl0843.34023MR1356893DOI10.1007/BF03322257
  16. 10.1016/S0096-3003(97)81653-0, Appl. Math. Comput. 89 (1998), 133–146. (1998) Zbl0910.34032MR1491699DOI10.1016/S0096-3003(97)81653-0
  17. 10.1016/0362-546X(94)90137-6, Nonlinear Anal., Theory Methods Appl. 23 (1994), 1427–1436. (1994) MR1306681DOI10.1016/0362-546X(94)90137-6
  18. 10.1006/jmaa.1995.1036, J.  Math. Anal. Appl. 189 (1995), 575–584. (1995) MR1312062DOI10.1006/jmaa.1995.1036
  19. Existence results for m -point boundary value problems, Differ. Equ. Dyn. Syst. 2 (1994), 289–298. (1994) MR1386275
  20. On the solvability of some multi-point boundary value problems, Appl. Math. 41 (1996), 1–17. (1996) MR1365136
  21. Existence results for multi-point boundary value problems for second order ordinary differential equations, Bull. Greek Math. Soc. 43 (2000), 105–123. (2000) MR1846952
  22. 10.1155/S1085337599000093, Abstr. Appl. Anal. 4 (1999), 71–81. (1999) MR1810319DOI10.1155/S1085337599000093
  23. 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. (1987) 
  24. Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator, Differ. Equ. 23 (1987), 979–987. (1987) 
  25. 10.1016/S0096-3003(02)00361-2, Appl. Math. Comput. 143 (2003), 275–299. (2003) Zbl1071.34014MR1981696DOI10.1016/S0096-3003(02)00361-2
  26. 10.1016/S0022-247X(02)00557-7, J.  Math. Anal. Appl. 277 (2003), 293–302. (2003) Zbl1026.34028MR1954477DOI10.1016/S0022-247X(02)00557-7
  27. Degree Theory, Cambridge University Press, Cambridge, 1978. (1978) Zbl0367.47001MR0493564
  28. Topological degree methods in nonlinear boundary value problems, In: NSF-CBMS Regional Conference Series in Math. No.  40, Americal Mathematical Society, Providence, 1979. (1979) Zbl0414.34025MR0525202
  29. 10.1515/ans-2004-0409, Adv. Nonlinear Stud. 4 (2004), 501–514. (2004) Zbl1082.47052MR2100911DOI10.1515/ans-2004-0409
  30. 10.1006/jmaa.1999.6441, J.  Math. Anal. Appl. 236 (1999), 384–398. (1999) MR1704590DOI10.1006/jmaa.1999.6441
  31. 10.1016/S0895-7177(01)00063-2, Math. Comput. Modelling 34 (2001), 311–318. (2001) MR1835829DOI10.1016/S0895-7177(01)00063-2

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.