Browse > Article
http://dx.doi.org/10.14317/jami.2015.749

EXISTENCE OF RADIAL POSITIVE SOLUTIONS FOR A QUSILINEAR NON-POSITONE PROBLEM IN A BALL  

WANG, WEIHUI (Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University)
YANG, ZUODONG (Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University)
Publication Information
Journal of applied mathematics & informatics / v.33, no.5_6, 2015 , pp. 749-757 More about this Journal
Abstract
In this paper, we prove existence of radial positive solutions for the following boundary value problem
Keywords
Existence; Radial Positive Solutions; Qusilinear Non-positone Problem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Guedda and L. Veron, Local and global properties of quasilinear elliptic equations, J. Diff. Eqs. 76 (1988), 159-189.   DOI
2 Zongming Guo, Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations, Applicable Anal. 47 (1992), 173-190.   DOI
3 Zongming Guo, Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems, Nonlinear Anal. 18 (1992), 957-971.   DOI
4 Zuodong Yang and Zongming Guo, On the structure of positive solutions for quasilinear ordinary differential equations, Appl. Anal. 58 (1995), 31-51.   DOI
5 J.A. Iaia, A priori estimates for a semilinear elliptic P.D.E, Nonlinear Anal. 24 (1995), 1039-1048.   DOI
6 Said Hakimi and Abderrahim Zertiti, Radial positive solutions for a nonpositone problem in a ball, Eletronic Journal of Differential Equations, 44 (2009), 1-6.
7 J.A. Iaia, A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems, Diff. Integral Eqns. 8 (1995), 393-403.
8 J.I. Diaz, Nonlinear Partial Differential Equations and Free Boundaries,Vol.I.Elliotic Equations, In Research Note in Math. Vol.106, Pitman, London, 1985.
9 S. Fucik, J. Necas and V. Soucek, Spectral analysis of nonlinear operators, Lecture Notes in Math. 346, Springer, Berlin, 1973.
10 Maya Chhetri and Petr Girg, Nonexistence of nonnegative solutions for a class of (p − 1)-superhomogeneous semipositone problems, J. Math. Anal. Appl. 322 (2006), 957-963.   DOI
11 Naji Yebari and Abderrahim Zertiti, Existence of non-negative solutions for nonlinear equations in the semi-positone case, Eletronic Journal of Differential Equations, 14 (2006), 249-254.
12 D.D. Hai and Haiyan Wang, Nontrivial solutions for p-Laplacian systems, J. Math. Anal. Appl. (2006), 1-9.
13 D.D. Hai and R. Shivaji, Existence and uniqueness for a class of quasilinear elliptic boundary value problems, J. Differential Equations, 193 (2003), 500-510.   DOI
14 W.M. Ni and J. Serrin, Nonexistence theorems for singular solutionsof quasilinear partial differential equations, Comm. Pure Appl. Math. 39 (1986), 379-399.   DOI
15 M. Garcia-Huidobro, R. Manasevich and K. Schmitt, Positive radial solutions of quasilinear elliptic partial differential equations in a ball, Nonlinear Anal. 35 (1999), 175-190.   DOI
16 Zuodong Yang, Existence of positive entire solutions for singular and non-singular quasilinear elliptic equation, J. Comput. Appl. Math. 197 (2006), 355-364.   DOI
17 Zuodong Yang and Qishao Lu, Asyptotics for quasilinear elliptic non-positone problems, Annales Polonici Mathematicl, (2002), 85-95.   DOI
18 L. Erbe and M. Tang, Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball, J. Differential Equations, 138 (1997), 351-379.   DOI
19 D.D. Hai and K. Schmitt, On radial solutions of quasilinear boundary value problems, Topics in Nonlinear Analysis, Progress in Nonlinear Differential Equations and their Applications, Birkhauser, Basel, 35 (1999), 349-361.
20 Zongming Guo,On the positive solutions for a class of quasilinear non-positone problems, Chinese Quarterly Math. 12 (1996), 1-11.
21 Zongming Guo and Zuodong Yang, Some uniqueness results for a class of quasilinear elliptic eigenvalue problems, Acta Math. Sinica(new series), 14 (1998), 245-260.   DOI
22 Zongming Guo and J.R.L. Webb, Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large, Proc. Roy. Soc. Edinburgh, 124A (1994), 189-198.   DOI
23 Zongming Guo and Z.D. Yang, Structure of positive solutions for quasilinear elliptic equation when a parameter is small, Chinese Ann. Math. 19 (1998), 385-392.
24 Zuodong Yang and Huisheng Yang, Asymptotics for a quasilinear elliptic partial differential equation, Archives of Inequalities and Applications, 1 (2003), 463-474.
25 A. Castro, M. Hassanpour and R. Shivaji, Uniqueness of nonnegative solutions for a semipositone problem with concave nonlinearity, Comm. Partial Differential Equations, 20 (1995), 1927-1936.   DOI
26 E.N. Dancer, On the number of positive solutions of weakly nonlinear elliptic equations when a parameter is large, Proc. London Math. Soc. 53 (1986), 429-452.
27 S.S. Lin, On the number of positive solutions for nonlinear elliptic equations when a parameter is large, Nonlinear Anal. 16 (1991), 283-297.   DOI
28 D.D. Hai, Uniqueness of positive solutions for a class of semilinear elliptic systems, Nonlinear Anal. 52 (2003), 595-603.   DOI
29 L. Erbe and M. Tang, Structure of positive radial solutions of semilinear elliptic equations, J. Differential Equations, 133 (1997), 179-202.   DOI
30 I. Ali, A. Castro and R. Shivaji, Uniqueness and stability of nonnegative solutions for semipositone problems in a ball, Proc. Amer. Math. Soc. 117 (1993), 775-782.   DOI
31 Zuodong Yang and Q.S. Lu, Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a quasilinear reaction-diffusion system, J. Computational and Appl. Math. 50 (2003), 37-56.   DOI
32 Zuodong Yang, Existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems, J. Math. Anal. Appl. 288 (2003), 768-783.   DOI
33 Zuodong Yang and Q.S. Lu, Blow-up estimates for a quasilinear reaction-diffusion system, Math. Methods in the Appl. Sci. 26 (2003), 1005-1023.   DOI
34 Xabier Garaizar, Existence of positive radial solutions for semilinear elliptic equations in the annulus, Journal of Differential Equations, 70 (1987), 69-72.   DOI