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ON POSITIVE SOLUTIONS FOR A CLASS OF INDEFINITE WEIGHT SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH CRITICAL SOBOLEV EXPONENT

  • Ko, Bong-Soo (Department of Mathematics Education Educational Research Institute Cheju National University) ;
  • Kang, Seung-Pil (Department of Mathematics Education Educational Research Institute Cheju National University)
  • Published : 2007.03.31

Abstract

By variational methods, we prove the existence of positive solutions of a class of indefinite weight semilinear elliptic boundary value problems on critical Sobolev exponent.

Keywords

References

  1. G. Afrouzi and K. Brown, On principal eigenvalues for boundary value problems with indefinite weight and Robin boundary conditions, Proc. Amer. Math. Soc. 127 (1999), no. 1, 125-130 https://doi.org/10.1090/S0002-9939-99-04561-X
  2. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437-477 https://doi.org/10.1002/cpa.3160360405
  3. N. Ghoussoub, Duality and perturbation methods in critical point theory, With appendices by David Robinson. Cambridge Tracts in Mathematics, 107. Cambridge University Press, Cambridge, 1993
  4. B. Ko and K. Brown, The existence of positive solutions for a class of indefinite weight semilinear elliptic boundary value problems, Nonlinear Anal. 39 (2000), no. 5, Ser. A: Theory Methods, 587-597 https://doi.org/10.1016/S0362-546X(98)00223-5
  5. R. Pohozaev, Eigenfunctions on the equation ${\Delta}$u + $\{lambda}$f(u) = 0, Soviet Math. Dokl. 6 (1965), 1408-1411