메뉴 건너뛰기




Volumn 249, Issue 7, 2010, Pages 1549-1578

Three positive solutions for Dirichlet problems involving critical Sobolev exponent and sign-changing weight

Author keywords

Concave convex nonlinearities; Critical Sobolev exponent; Fibering map; Lusternik Schnirelman category; Sign changing weight

Indexed keywords


EID: 77955570947     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2010.07.021     Document Type: Article
Times cited : (29)

References (30)
  • 1
    • 0003288355 scopus 로고
    • Critical points and nonlinear variational problems
    • Ambrosetti A. Critical points and nonlinear variational problems. Mem. Soc. Math. Fr. (N.S.) 1992, 49.
    • (1992) Mem. Soc. Math. Fr. (N.S.) , vol.49
    • Ambrosetti, A.1
  • 2
    • 0030577835 scopus 로고    scopus 로고
    • Multiplicity results for some nonlinear elliptic equations
    • Ambrosetti A., Azorero G.J., Peral I. Multiplicity results for some nonlinear elliptic equations. J. Funct. Anal. 1996, 137:219-242.
    • (1996) J. Funct. Anal. , vol.137 , pp. 219-242
    • Ambrosetti, A.1    Azorero, G.J.2    Peral, I.3
  • 3
    • 0000049245 scopus 로고
    • Combined effects of concave and convex nonlinearities in some elliptic problems
    • Ambrosetti A., Brezis H., Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J. Funct. Anal. 1994, 122:519-543.
    • (1994) J. Funct. Anal. , vol.122 , pp. 519-543
    • Ambrosetti, A.1    Brezis, H.2    Cerami, G.3
  • 4
    • 0004435491 scopus 로고    scopus 로고
    • Four positive solutions for the semilinear elliptic equation: -Δu+u=a(x)up+f(x) in RN
    • Adachi S., Tanaka K. Four positive solutions for the semilinear elliptic equation: -Δu+u=a(x)up+f(x) in RN. Calc. Var. Partial Differential Equations 2000, 11:63-95.
    • (2000) Calc. Var. Partial Differential Equations , vol.11 , pp. 63-95
    • Adachi, S.1    Tanaka, K.2
  • 5
    • 0000343907 scopus 로고    scopus 로고
    • On the number of positive solutions of some semilinear Dirichlet problems in a ball
    • Adimurthy, Pacella F., Yadava L. On the number of positive solutions of some semilinear Dirichlet problems in a ball. Differential Integral Equations 1997, 10(6):1157-1170.
    • (1997) Differential Integral Equations , vol.10 , Issue.6 , pp. 1157-1170
    • Adimurthy1    Pacella, F.2    Yadava, L.3
  • 6
    • 84990623267 scopus 로고
    • On a nonlinear equation involving the critical Sobolev exponent: the effect of the topology of the domain
    • Bahri A., Coron J.M. On a nonlinear equation involving the critical Sobolev exponent: the effect of the topology of the domain. Comm. Pure Appl. Math. 1988, 41:253-294.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 253-294
    • Bahri, A.1    Coron, J.M.2
  • 8
    • 84941275804 scopus 로고
    • A relation between pointwise convergence of functions and convergence of functionals
    • Brézis H., Lieb E.H. A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 1983, 88:486-490.
    • (1983) Proc. Amer. Math. Soc. , vol.88 , pp. 486-490
    • Brézis, H.1    Lieb, E.H.2
  • 9
    • 0345293985 scopus 로고
    • A minimization problem with critical exponent and non zero data
    • Symmetry in Nature
    • Brezis H., Nirenberg L. A minimization problem with critical exponent and non zero data. Ann. Sc. Norm. Super. Pisa Cl. 1989, 129-140.
    • (1989) Ann. Sc. Norm. Super. Pisa Cl. , pp. 129-140
    • Brezis, H.1    Nirenberg, L.2
  • 10
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • Brezis H., Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 1983, 16:437-477.
    • (1983) Comm. Pure Appl. Math. , vol.16 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 11
    • 34248386093 scopus 로고    scopus 로고
    • A fibering map approach to a semilinear elliptic boundary value problem
    • Brown K.J., Wu T.F. A fibering map approach to a semilinear elliptic boundary value problem. Electron. J. Differential Equations 2007, 69:1-9.
    • (2007) Electron. J. Differential Equations , vol.69 , pp. 1-9
    • Brown, K.J.1    Wu, T.F.2
  • 12
    • 74349100195 scopus 로고    scopus 로고
    • A fibering map approach to a potential operator equation and its applications
    • Brown K.J., Wu T.F. A fibering map approach to a potential operator equation and its applications. Differential Integral Equations 2009, 22:1097-1114.
    • (2009) Differential Integral Equations , vol.22 , pp. 1097-1114
    • Brown, K.J.1    Wu, T.F.2
  • 13
    • 0041351871 scopus 로고    scopus 로고
    • The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function
    • Brown K.J., Zhang Y. The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function. J. Differential Equations 2003, 193:481-499.
    • (2003) J. Differential Equations , vol.193 , pp. 481-499
    • Brown, K.J.1    Zhang, Y.2
  • 14
    • 0000206097 scopus 로고
    • Topologie et cas limite des injections de Sobolev
    • Coron J.M. Topologie et cas limite des injections de Sobolev. C. R. Acad. Sci. Paris Ser. I 1984, 299:209-212.
    • (1984) C. R. Acad. Sci. Paris Ser. I , vol.299 , pp. 209-212
    • Coron, J.M.1
  • 15
    • 0003326091 scopus 로고    scopus 로고
    • Quasilinear Elliptic Equations with Degenerations and Singularities
    • Walter de Gruyter, New York, Berlin
    • Drábek P., Kufner A., Nicolosi F. Quasilinear Elliptic Equations with Degenerations and Singularities. Ser. Nonlinear Anal. Appl. 1997, vol. 5. Walter de Gruyter, New York, Berlin.
    • (1997) Ser. Nonlinear Anal. Appl. , vol.5
    • Drábek, P.1    Kufner, A.2    Nicolosi, F.3
  • 16
    • 21744435093 scopus 로고    scopus 로고
    • Positive solutions for the p-Laplacian: application of the fibering method
    • Drábek P., Pohozaev S.I. Positive solutions for the p-Laplacian: application of the fibering method. Proc. Roy. Soc. Edinburgh 1997, 127:703-726.
    • (1997) Proc. Roy. Soc. Edinburgh , vol.127 , pp. 703-726
    • Drábek, P.1    Pohozaev, S.I.2
  • 17
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland I. On the variational principle. J. Math. Anal. Appl. 1974, 17:324-353.
    • (1974) J. Math. Anal. Appl. , vol.17 , pp. 324-353
    • Ekeland, I.1
  • 18
    • 0038706295 scopus 로고    scopus 로고
    • Local superlinearity and sublinearity for indefinite semilinear elliptic problems
    • de Figueiredo D.G., Gossez J.P., Ubilla P. Local superlinearity and sublinearity for indefinite semilinear elliptic problems. J. Funct. Anal. 2003, 199:452-467.
    • (2003) J. Funct. Anal. , vol.199 , pp. 452-467
    • de Figueiredo, D.G.1    Gossez, J.P.2    Ubilla, P.3
  • 19
    • 56049089199 scopus 로고    scopus 로고
    • Positive solutions for critical inhomogeneous elliptic problems in non-contractible domains
    • He H., Yang J. Positive solutions for critical inhomogeneous elliptic problems in non-contractible domains. Nonlinear Anal. 2009, 70:952-973.
    • (2009) Nonlinear Anal. , vol.70 , pp. 952-973
    • He, H.1    Yang, J.2
  • 20
    • 84980167932 scopus 로고
    • Remark on some quasilinear elliptic equations
    • Kazdan J., Warner F. Remark on some quasilinear elliptic equations. Comm. Pure Appl. Math. 1975, 28:567-597.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 567-597
    • Kazdan, J.1    Warner, F.2
  • 21
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The limit case
    • Lions P.L. The concentration-compactness principle in the calculus of variations. The limit case. Rev. Mat. Iberoamericana. Rev. Mat. Iberoamericana 1985, 2:45-121.
    • (1985) Rev. Mat. Iberoamericana. Rev. Mat. Iberoamericana , vol.2 , pp. 45-121
    • Lions, P.L.1
  • 22
    • 0002608722 scopus 로고    scopus 로고
    • Exact multiplicity of positive solutions for a class of semilinear problem II
    • Ouyang T., Shi J. Exact multiplicity of positive solutions for a class of semilinear problem II. J. Differential Equations 1999, 158:94-151.
    • (1999) J. Differential Equations , vol.158 , pp. 94-151
    • Ouyang, T.1    Shi, J.2
  • 23
    • 0001901435 scopus 로고
    • Minimax Methods in Critical Point Theory with Applications to Differential Equations
    • American Mathematical Society
    • Rabinowitz P.H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. Reg. Conf. Ser. Math. 1986, American Mathematical Society.
    • (1986) Reg. Conf. Ser. Math.
    • Rabinowitz, P.H.1
  • 24
    • 0004118642 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin, Heidelberg
    • Struwe M. Variational Methods 1996, Springer-Verlag, Berlin, Heidelberg. second ed.
    • (1996) Variational Methods
    • Struwe, M.1
  • 25
    • 85013168104 scopus 로고
    • On nonhomogeneous elliptic involving critical Sobolev exponent
    • Tarantello G. On nonhomogeneous elliptic involving critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Lineairé 1992, 9(3):281-304.
    • (1992) Ann. Inst. H. Poincaré Anal. Non Lineairé , vol.9 , Issue.3 , pp. 281-304
    • Tarantello, G.1
  • 26
    • 1442307581 scopus 로고    scopus 로고
    • Exact multiplicity for semilinear elliptic Dirichlet problems involving concave and convex nonlinearities
    • Tang M. Exact multiplicity for semilinear elliptic Dirichlet problems involving concave and convex nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A 2003, 133:705-717.
    • (2003) Proc. Roy. Soc. Edinburgh Sect. A , vol.133 , pp. 705-717
    • Tang, M.1
  • 27
    • 84981761946 scopus 로고
    • On Harnack type inequalities and their application to quasilinear elliptic equations
    • Trudinger N.S. On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math. 1967, 20:721-747.
    • (1967) Comm. Pure Appl. Math. , vol.20 , pp. 721-747
    • Trudinger, N.S.1
  • 29
    • 69549135550 scopus 로고    scopus 로고
    • Multiplicity results for a semilinear elliptic equation involving sign-changing weight function
    • Wu T.F. Multiplicity results for a semilinear elliptic equation involving sign-changing weight function. Rocky Mountain J. Math. 2009, 39:995-1012.
    • (2009) Rocky Mountain J. Math. , vol.39 , pp. 995-1012
    • Wu, T.F.1
  • 30
    • 42149166006 scopus 로고    scopus 로고
    • On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function
    • Wu T.F. On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function. Commun. Pure Appl. Anal. 2008, 7:383-405.
    • (2008) Commun. Pure Appl. Anal. , vol.7 , pp. 383-405
    • Wu, T.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.