Browse > Article
http://dx.doi.org/10.4134/JKMS.2013.50.4.797

POSITIVE SOLUTIONS OF SINGULAR DIRICHLET PROBLEMS VIA VARIATIONAL METHODS  

Sun, Juntao (School of Science, Shandong University of Technology)
Chu, Jifeng (Department of Mathematics, College of Science, Hohai University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 797-811 More about this Journal
Abstract
In this paper, we establish the existence results for second order singular Dirichlet problems via variational methods. Some recent results are extended and improved. Examples are also given to illustrate the new results.
Keywords
positive solutions; singular Dirichlet problems; variational methods; critical points;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. P. Agarwal and D. O'Regan, Singular Differential and Integral Equations with Ap-plications, Kluwer Academic Publishers, Dordrecht, 2003.
2 R. P. Agarwal and D. O'Regan, Singular boundary value problems for superlinear second order ordinary and delay differential equations, J. Differential Equations 130 (1996), no. 2, 333-355.   DOI   ScienceOn
3 R. P. Agarwal and D. O'Regan, Existence theory for single and multiple solutions to singular positone boundary value problems, J. Differential Equations 175 (2001), no. 2, 393-414.   DOI   ScienceOn
4 R. P. Agarwal and D. O'Regan, Existence criteria for singular boundary value problems with sign changing nonlinearities, J. Differential Equations 183 (2002), no. 2, 409-433.   DOI   ScienceOn
5 R. P. Agarwal, K. Perera, and D. O'Regan, Multiple positive solutions of singular problems by variational methods, Proc. Amer. Math. Soc. 134 (2006), no. 3, 817-824.   DOI   ScienceOn
6 R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Clarendon Press, 8, Oxford, 1975.
7 J. V. Baxley, A singular nonlinear boundary value problem: membrane response of a spherical cap, SIAM J. Appl. Math. 48 (1988), no. 3, 497-505.   DOI   ScienceOn
8 G. Bonanno and G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl. 2009 (2009), Article ID 670675, 20 pages.
9 G. Bonanno and B. Di Bella, Infinitely many solutions for a fourth-order elastic beam equation, Nonlinear Differential Equations Appl. 18 (2011), no. 3, 357-368.   DOI
10 A. Callegari and A. Nachman, Some singular nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64 (1978), no. 1, 96-105.   DOI   ScienceOn
11 J. Chu and D. O'Regan, Multiplicity results for second order non-autonomous singular Dirichlet systems, Acta Appl. Math. 105 (2009), no. 3, 323-338.   DOI
12 J. A . Cid, O. L. Pouso, and R. L. Pouso, Existence of infinitely many solutions for second-order singular initial value problems with an application to nonlinear massive gravity, Nonlinear Anal. Real World Appl. 12 (2011), no. 5, 2596-2606.   DOI   ScienceOn
13 L. Erbe and R. Mathsen, Positive solutions for singular nonlinear boundary value problems, Nonlinear Anal. 46 (2001), no. 7, 979-986.   DOI   ScienceOn
14 P. Habets and F. Zanolin, Upper and lower solutions for a generalized Emden-Fowler equation, J. Math. Anal. Appl. 181 (1994), no. 3, 684-700.   DOI   ScienceOn
15 X. He and W. Zou, Infinitely many solutions for a singular elliptic equation involving critical sobolev-Hardy exponents in $\mathbb{R}^n$, Acta Math. Sci. Ser. B Engl. Ed. 30 (2010), no. 3, 830-840.
16 A. Nachman and A. Callegari, A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), no. 2, 275-282.   DOI   ScienceOn
17 K. Lan, Multiple positive solutions of semilinear differential equations with singularities, J. London Math. Soc. (2) 63 (2001), no. 3, 690-704.   DOI
18 K. Lan and J. R. Webb, Positive solutions of semilinear differential equations with singularities, J. Differential Equations 148 (1998), no. 2, 407-421.   DOI   ScienceOn
19 J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, 1989.
20 S. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), no. 6, 897-904.   DOI   ScienceOn
21 E. Zeidler, Nonlinear Functional Analysis and its Applications. III, Springer-Verlag, 1985.