DOI QR코드

DOI QR Code

MULTIPLE EXISTENCE OF POSITIVE GLOBAL SOLUTIONS FOR PARAMETERIZED NONHOMOGENEOUS ELLIPTIC EQUATIONS INVOLVING CRITICAL EXPONENTS

  • Kim, Wan Se (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University)
  • 투고 : 2014.03.25
  • 심사 : 2014.05.26
  • 발행 : 2014.05.31

초록

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

키워드

참고문헌

  1. A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funt. Anal., 14 (1973), 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
  2. S. Bae, Positive global solutions of inhomogenuous semilinear elliptic equations with critical sobolev exponent, Preprint.
  3. H. Brezis and E. Lieb, A relation between pointwise convergence of functionals and convergence of functions,, Proc. Amer. Soc., 88 (1983), 486-490. https://doi.org/10.1090/S0002-9939-1983-0699419-3
  4. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponent, Comm. Pure Appl. Math., 36 (1983), 437-427. https://doi.org/10.1002/cpa.3160360405
  5. D.-M. Cao, Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equations on $\mathbb{R}^N$, Nonlinear Anal. T.M.A., 15(1990), 1048-1052.
  6. Y. Deng and Li. Y, Existence and bifurcation of positive solutions for a semilinear elliptic equation with critical exponent, J. Diff. Equa., 130 (1996), 179-200. https://doi.org/10.1006/jdeq.1996.0138
  7. Y. Deng and Li. Y, Existence of multiple positive solutions for a semilinear elliptic equation, Adv. Differential Equations, 2(1997), 361-382.
  8. W.-Y. Ding and W.-M. Ni On the existence of positive solutions for a semilinear elliptic equation, Archs Ration Mech. Analysis, 91(1986), 283-307. https://doi.org/10.1007/BF00282336
  9. L. Ekeland, Convex minimization problem, Bull. Amer. Math. Soc., (NS)1 (1976), 443-474.
  10. L. Caffarely, G. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math 42(1986), 271-1191.
  11. N. Hirano, Existence of entire positive solutions for nonhomogeneous elliptic equations, Nonlinear Analysis. T.M.A., 29(8) (1997), 889-901. https://doi.org/10.1016/S0362-546X(96)00176-9
  12. N. Hirano, Multiple existence of solutions for a nonhomogeneous elliptic problems on $\mathbb{R}^N$, J. Math. Anal. Appl., 336 (2007), 506-522. https://doi.org/10.1016/j.jmaa.2007.02.070
  13. N. Hirano and W. S. Kim, Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on $\mathbb{R}^N$, J. Diff. Equa, 249,(2010), 1799-1816. https://doi.org/10.1016/j.jde.2010.05.003
  14. N. Hirano and W. S. Kim, Multiple existence of solutions for a nonhomogeneous elliptic problem on $\mathbb{R}^N$, Nonlinear Analysis. T.M.A., 74,(2011), 4369-4378. https://doi.org/10.1016/j.na.2011.03.042
  15. M. K. Kwong, Uniqueness of positive solution of ${\Delta}u- u+u^p=0\;in\;R^N$, Arch. Retional Mech. Anal. 105(3), (1989), 243-266.
  16. P.L. Lions, The concentration-compactness principle in the calculus of variations, the locally compact case. part 1, Ann. Inst. H. Poincare Analyse non Lineaire, 1(2)(1984), 109-145,. https://doi.org/10.1016/S0294-1449(16)30428-0
  17. P.L. Lions, The concentration-compactness principle in the calculus of variations, the locally compact case. part 2, Ann. Inst. H. Poincare Analyse non Lineaire, 1(4)(1984), 223-283,. https://doi.org/10.1016/S0294-1449(16)30422-X
  18. W.A. Strauss, Existence of solatary waves in higher dimensions, Communs. Math. Phys., 55(1977), 149-162. https://doi.org/10.1007/BF01626517
  19. M. Willem, Minimax theorems, Birkhauser. Boston, Basel, Berlin. (1996).
  20. X.-P. Zhu, Multiple entire solutions of a semilinear elliptic equation, Nonlinear analysis T.M.A., 12(11) (1988), 1297-1316. https://doi.org/10.1016/0362-546X(88)90061-2
  21. X.-P. Zhu, A perturbation result on positive entire solutions of a semilinear elliptic equation, J. Diff. Equa, 92 (1991) 163-178. https://doi.org/10.1016/0022-0396(91)90045-B
  22. X.-P. Zhu, and H.-S. Zhu, Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domain , Proc. Roy. Soc. Edinburgh , 115 A (1990) 301-318.

피인용 문헌

  1. PARAMETRIZED PERTURBATION RESULTS ON GLOBAL POSITIVE SOLUTIONS FOR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS AND HARDY TEREMS vol.34, pp.5, 2014, https://doi.org/10.7858/eamj.2018.035