57
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Solvability of Boundary Value Problems for Singular Quasi-Laplacian Differential Equations on the Whole Line

Pages 423-446 | Received 06 Jul 2011, Accepted 12 Apr 2012, Published online: 25 May 2012

References

  • Agarwal , R.P. 1986 . Boundary Value Problems for Higher Order Differential Equations , Singapore : World Scientific .
  • Avramescu , C. and Vladimirescu , C. 2002 . Limits of solutions of a perturbed linear differential equation. Electron . J. Qual. Theory Differ. Equ. , 3 : 1 – 11 .
  • Avramescu , C. and Vladimirescu , C. 2004 . Existence of solutions to second order ordinary differential equations having finite limits at ±8 . Electron. J. Differential Equations , 18 : 1 – 12 .
  • Avramescu , C. and Vladimirescu , C. 2008 . Existence of homoclinic solutions to a non-linear second order ODE, dynamics of continuous, discrete and impulsive systems . Ser. A. Math. Anal. , 15 : 481 – 491 .
  • B. Bianconi and F. Papalini Non-autonomous boundary value problems on the real line . Discrete Contin. Dyn. Syst. , 15 : 759 – 776 , 2006 . http://dx.doi.org/10.3934/dcds.2006.15.759 .
  • A. Cabada and J.A. Cid Heteroclinic solutions for non-autonomous boundary value problems with singular F-Laplacian operators . In Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference , Discrete Contin, Dyn. Syst., suppl ., pp. 118 – 122 , 2009 .
  • A. Calamai . Heteroclinic solutions of boundary value problems on the real line involving singular F-Laplacian operators . J. Math. Anal. Appl ., 378 : 667 – 679 , 2011 . http://dx.doi.org/10.1016/j.jmaa.2011.01.056 .
  • Chamberlain , J. , Kong , L. and Kong , Q. 2009 . Nodal solutions of nonlocal boundary value problems . Mathematical Modelling and Applications , 14 : 435 – 450 .
  • Čiegis , R. , Štikonas , A. , Štikonieneė , O. and Suboč , O. 2001 . Stationary problems with nonlocal boundary conditions . Math. Model. Anal. , 6 ( 2 ) : 178 – 191 .
  • Čiegis , R. and Tumanova , N. 2010 . Numerical solution of parabolic problems with nonlocal boundary conditions . Numerical Functional Analysis and Optimization , 31 ( 10 ) : 1318 – 1329 .
  • Cupini , G. , Marcelli , C. and Papalini , F. 2011 . Heteroclinic solutions of boundary value problems on the real line involving general nonlinear differential operators . Differential Integral Equations , 24 : 619 – 644 .
  • Cupini , G. , Marcelli , C. and Papalini , F. 2011 . On the solvability of a boundary value problem on the real line . Bound. Value Probl , 26 : 1 – 17 .
  • K. Deimling . Nonlinear Functional Analysis . Springer , Berlin , , Germany , 1985 .
  • Ge , W. 2007 . Boundary Value Problems for Ordinary Differential Equations , Beijing : Science Press .
  • Il'in , V.A. and Moiseev , E.I. 1987 . Nonlocal boundary-value problem of the second kind for a Sturm–Liouville operator . Differ. Equ. , 23 : 979 – 987 .
  • C. Marcelli and F. Papalini . Heteroclinic connections for fully non-linear non-autonomous second-order differential equations . J. Differential Equations , 241 : 160 – 183 , 2007 . http://dx.doi.org/10.1016/j.jde.2007.05.038 .
  • Philos , C.G. and Purnaras , I.K. 2010 . A boundary value problem on the whole line to second order nonlinear differential equations . Georgian Math. J. , 17 : 241 – 252 .
  • Rachunkova , I. , Stanek , S. and Tvrdy , M. 2006 . “ Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equations ” . In Handbook of Differential Equations, Ordinary Differential Equations , Edited by: Canada , A. , Drabek , P. and Fonde , A. Vol. 3 , 606 – 723 . Elsevier .
  • Wang , Y. and Ge , W. 2007 . Existence of triple positive solutions for multi-point boundary value problems with a one dimensional p-Laplacian . Computers and Mathematics with Applications , 54 : 793 – 807 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.