메뉴 건너뛰기




Volumn 198, Issue 1, 2004, Pages 91-128

A convex-concave problem with a nonlinear boundary condition

Author keywords

Critical exponents; Nonlinear boundary conditions

Indexed keywords


EID: 1542615710     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00068-8     Document Type: Article
Times cited : (84)

References (32)
  • 1
    • 0036993227 scopus 로고    scopus 로고
    • Some results for semilinear elliptic equations with critical potential
    • B. Abdellaoui, I. Peral, Some results for semilinear elliptic equations with critical potential, Proc. Royal Soc. Edinburgh 132A (2002) 1-24.
    • (2002) Proc. Royal Soc. Edinburgh , vol.132 A , pp. 1-24
    • Abdellaoui, B.1    Peral, I.2
  • 2
    • 43949176286 scopus 로고
    • Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity
    • Adimurthi, F. Pacella, S.L. Yadava, Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal. 113 (1993) 318-350.
    • (1993) J. Funct. Anal. , vol.113 , pp. 318-350
    • Adimurthi, A.1    Pacella, F.2    Yadava, S.L.3
  • 3
    • 0000049245 scopus 로고
    • Combined effects of concave and convex nonlinearities in some elliptic problems
    • A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994) 519-543.
    • (1994) J. Funct. Anal. , vol.122 , pp. 519-543
    • Ambrosetti, A.1    Brezis, H.2    Cerami, G.3
  • 4
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and applications
    • A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (4) (1973) 349-381.
    • (1973) J. Funct. Anal. , vol.14 , Issue.4 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.H.2
  • 5
    • 84963421267 scopus 로고
    • Does bifurcation from the essential spectrum occur?
    • V. Benci, D. Fortunato, Does bifurcation from the essential spectrum occur?, Comm. Partial Differential Equations 6 (3) (1981) 249-272.
    • (1981) Comm. Partial Differential Equations , vol.6 , Issue.3 , pp. 249-272
    • Benci, V.1    Fortunato, D.2
  • 6
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • H. Brezis, L. Niremberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. XXXVI (1983) 437-477.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 437-477
    • Brezis, H.1    Niremberg, L.2
  • 7
    • 0001231329 scopus 로고
    • Problèmes de Neumann non linéaires sur les variétés Riemanniennes
    • P. Cherrier, Problèmes de Neumann non linéaires sur les variétés Riemanniennes, J. Funct. Anal. 57 (1984) 154-206.
    • (1984) J. Funct. Anal. , vol.57 , pp. 154-206
    • Cherrier, P.1
  • 9
    • 0002634193 scopus 로고
    • Stationary solutions, blow-up and convergence to stationary solutions for a semilinear parabolic equation with nonlinear boundary conditions
    • M. Chipot, M. Fila, P. Quittner, Stationary solutions, blow-up and convergence to stationary solutions for a semilinear parabolic equation with nonlinear boundary conditions, Acta Math. Univ. Comenian. 60 (1991) 35-103.
    • (1991) Acta Math. Univ. Comenian. , vol.60 , pp. 35-103
    • Chipot, M.1    Fila, M.2    Quittner, P.3
  • 10
    • 0002632932 scopus 로고    scopus 로고
    • On the solutions to some elliptic equations with nonlinear boundary conditions
    • M. Chipot, I. Shafrir, M. Fila, On the solutions to some elliptic equations with nonlinear boundary conditions, Adv. Differential Equations 1 (1) (1996) 91-110.
    • (1996) Adv. Differential Equations , vol.1 , Issue.1 , pp. 91-110
    • Chipot, M.1    Shafrir, I.2    Fila, M.3
  • 11
    • 51249191299 scopus 로고
    • A minimum-maximum principle for a class of nonlinear integral equations
    • C.V. Coffman, A minimum-maximum principle for a class of nonlinear integral equations, J. Anal. Math. 22 (1969) 391-419.
    • (1969) J. Anal. Math. , vol.22 , pp. 391-419
    • Coffman, C.V.1
  • 12
    • 0033164959 scopus 로고    scopus 로고
    • Uniqueness and nonuniqueness for a system of heat equations with nontrivial coupling at the boundary
    • C. Cortazar, M. Elgueta, J.D. Rossi, Uniqueness and nonuniqueness for a system of heat equations with nontrivial coupling at the boundary, Nonlinear Anal. 37 (2) (1999) 257-267.
    • (1999) Nonlinear Anal. , vol.37 , Issue.2 , pp. 257-267
    • Cortazar, C.1    Elgueta, M.2    Rossi, J.D.3
  • 13
    • 84990613846 scopus 로고
    • Uniqueness theorems on conformal deformations of metrics, Sobolev inequalities, and an eigenvalue estimate
    • J.F. Escobar, Uniqueness theorems on conformal deformations of metrics, Sobolev inequalities, and an eigenvalue estimate, Comm. Pure Appl. Math. 43 (1990) 857-883.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 857-883
    • Escobar, J.F.1
  • 14
    • 0002416517 scopus 로고
    • Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature
    • J.F. Escobar, Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature, Ann. of Math. 136 (2) (1992) 1-50.
    • (1992) Ann. of Math. , vol.136 , Issue.2 , pp. 1-50
    • Escobar, J.F.1
  • 15
    • 0013078894 scopus 로고    scopus 로고
    • Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains
    • C. Flores, M. del Pino, Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains, Comm. Partial Differential Equations 26 (11-12) (2001) 2189-2210.
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.11-12 , pp. 2189-2210
    • Flores, C.1    del Pino, M.2
  • 16
    • 84968483586 scopus 로고
    • Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term
    • J. Garcia-Azorero, I. Peral, Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Trans. Amer. Math. Soc. 323 (2) (1991) 877-895.
    • (1991) Trans. Amer. Math. Soc. , vol.323 , Issue.2 , pp. 877-895
    • Garcia-Azorero, J.1    Peral, I.2
  • 17
    • 0001682809 scopus 로고
    • A general mountain pass principle for locating and classifying critical points
    • N. Ghoussoub, D. Preiss, A general mountain pass principle for locating and classifying critical points, Ann. Inst. H. Poincaré, Anal. Non Linéaire 6 (5) (1989) 321-330.
    • (1989) Ann. Inst. H. Poincaré, Anal. Non Linéaire , vol.6 , Issue.5 , pp. 321-330
    • Ghoussoub, N.1    Preiss, D.2
  • 18
    • 84972539381 scopus 로고
    • Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition
    • B. Hu, Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition, Differential Integral Equations 7 (2) (1994) 301-313.
    • (1994) Differential Integral Equations , vol.7 , Issue.2 , pp. 301-313
    • Hu, B.1
  • 19
    • 84968468748 scopus 로고
    • The profile near blow-up time for the solution of the heat equation with a nonlinear boundary condition
    • B. Hu, Hong-Ming Yin, The profile near blow-up time for the solution of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1) (1994) 117-135.
    • (1994) Trans. Amer. Math. Soc. , vol.346 , Issue.1 , pp. 117-135
    • Hu, B.1    Yin, H.-M.2
  • 21
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The limit case, Part 1
    • P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Part 1, Rev. Mat. Iberoamericana. 1 (1) (1985) 145-201.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , Issue.1 , pp. 145-201
    • Lions, P.L.1
  • 22
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The limit case, Part 2
    • P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Part 2, Rev. Mat. Iberoamericana. 1 (2) (1985) 45-121.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , Issue.2 , pp. 45-121
    • Lions, P.L.1
  • 23
    • 0012982592 scopus 로고
    • Best constants in Sobolev inequalities for functions vanishing on some part of the boundary and related questions
    • P.L. Lions, F. Pacella, M. Tricarico, Best constants in Sobolev inequalities for functions vanishing on some part of the boundary and related questions, Indiana Univ. Math. J. 37 (2) (1988) 301-324.
    • (1988) Indiana Univ. Math. J. , vol.37 , Issue.2 , pp. 301-324
    • Lions, P.L.1    Pacella, F.2    Tricarico, M.3
  • 24
    • 0034656488 scopus 로고    scopus 로고
    • Existence and nonexistence of solutions for quasilinear elliptic equations
    • M. Montenegro, M. Montenegro, Existence and nonexistence of solutions for quasilinear elliptic equations, J. Math. Anal. Appl. 245 (2000) 303-316.
    • (2000) J. Math. Anal. Appl. , vol.245 , pp. 303-316
    • Montenegro, M.1    Montenegro, M.2
  • 25
    • 0041141622 scopus 로고
    • On a Neumann problem with critical exponent and critical nonlinearity on the boundary
    • D. Pierrotti, S. Terracini, On a Neumann problem with critical exponent and critical nonlinearity on the boundary, Comm. Partial Differential Equations 20 (7&8) (1995) 1155-1187.
    • (1995) Comm. Partial Differential Equations , vol.20 , Issue.7-8 , pp. 1155-1187
    • Pierrotti, D.1    Terracini, S.2
  • 26
    • 0001901435 scopus 로고
    • Minimax methods in critical point theory with applications to differential equations
    • American Mathematical Society, Providence, RI
    • P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, in: CBMS Regional Conference Series in Mathematics; Vol. 65, American Mathematical Society, Providence, RI, 1986.
    • (1986) CBMS Regional Conference Series in Mathematics , vol.65
    • Rabinowitz, P.1
  • 27
    • 0001264525 scopus 로고    scopus 로고
    • Blow-up results and localization of blow-up points in an n-dimensional smooth domain
    • D.F. Rial, J.D. Rossi, Blow-up results and localization of blow-up points in an n-dimensional smooth domain, Duke Math. J. 88 (2) (1997) 391-405.
    • (1997) Duke Math. J. , vol.88 , Issue.2 , pp. 391-405
    • Rial, D.F.1    Rossi, J.D.2
  • 28
    • 34347203011 scopus 로고
    • Problemi al contorno ellitici, con dati discontinui, dotati di soluzioni hölderiane, (Italian)
    • G. Stampacchia, Problemi al contorno ellitici, con dati discontinui, dotati di soluzioni hölderiane, (Italian), Ann. Mat. Pura Appl. 51 (4) (1960) 1-37.
    • (1960) Ann. Mat. Pura Appl. , vol.51 , Issue.4 , pp. 1-37
    • Stampacchia, G.1
  • 29
    • 0006796629 scopus 로고
    • Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions
    • S. Terraccini, Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions, Differential Integral Equations 8 (8) (1995) 1911-1922.
    • (1995) Differential Integral Equations , vol.8 , Issue.8 , pp. 1911-1922
    • Terraccini, S.1
  • 30
    • 0000471156 scopus 로고
    • Remarks concerning the conformal deformation of Riemannian structures on compact manifolds
    • N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968) 265-274.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 265-274
    • Trudinger, N.1
  • 31
    • 0003088926 scopus 로고
    • On Existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition
    • W. Walter, On Existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition, SIAM J. Math. Anal. 6 (1) (1975) 85-90.
    • (1975) SIAM J. Math. Anal. , vol.6 , Issue.1 , pp. 85-90
    • Walter, W.1
  • 32
    • 0001173375 scopus 로고
    • Neumann problems of semilinear elliptic equations involving critical Sobolev exponents
    • Xu-Jia Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations 93 (1991) 283-310.
    • (1991) J. Differential Equations , vol.93 , pp. 283-310
    • Wang, X.-J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.