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Volumn 22, Issue 2, 2005, Pages 187-206

Nonlinear eigenvalues and bifurcation problems for Pucci's operators

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COERCIVE FORCE; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 13844322232     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2004.05.004     Document Type: Article
Times cited : (92)

References (36)
  • 1
    • 0035371795 scopus 로고    scopus 로고
    • Propagation of maxima and strong maximum principle for viscosity solution of degenerate elliptic equation I: Convex operators
    • M. Bardi, and F. Da Lio Propagation of maxima and strong maximum principle for viscosity solution of degenerate elliptic equation I: convex operators Nonlinear Anal. 44 2001 991 1006
    • (2001) Nonlinear Anal. , vol.44 , pp. 991-1006
    • Bardi, M.1    Da Lio, F.2
  • 2
    • 0042175104 scopus 로고
    • Applications of Variational Inequalities in Stochastic Control
    • North-Holland Amsterdam
    • A. Bensoussan, and J.L. Lions Applications of Variational Inequalities in Stochastic Control Stud. Math. Appl. 12 1982 North-Holland Amsterdam Translated from the French
    • (1982) Stud. Math. Appl. 12
    • Bensoussan, A.1    Lions, J.L.2
  • 3
    • 0000324980 scopus 로고
    • On some nonlinear Sturm-Liouville problems
    • H. Berestycki On some nonlinear Sturm-Liouville problems J. Differential Equations 26 3 1977 375 390
    • (1977) J. Differential Equations , vol.26 , Issue.3 , pp. 375-390
    • Berestycki, H.1
  • 4
    • 13844311748 scopus 로고
    • On the method of moving planes and the sliding method
    • H. Berestycki, and L. Nirenberg On the method of moving planes and the sliding method Boll. Soc. Brasil Mat. (N.S.) 22 1991 237 275
    • (1991) Boll. Soc. Brasil Mat. (N.S.) , vol.22 , pp. 237-275
    • Berestycki, H.1    Nirenberg, L.2
  • 5
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second-order elliptic operators in general domains
    • H. Berestycki, L. Nirenberg, and S.R.S. Varadhan The principal eigenvalue and maximum principle for second-order elliptic operators in general domains Comm. Pure Appl. Math. 47 1 1994 47 92
    • (1994) Comm. Pure Appl. Math. , vol.47 , Issue.1 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 7
    • 84990557319 scopus 로고
    • The Dirichlet problem for nonlinear second order elliptic equations II
    • L. Caffarelli, J.J. Kohn, L. Nirenberg, and J. Spruck The Dirichlet problem for nonlinear second order elliptic equations II Comm. Pure Appl. Math. 38 1985 209 252
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 209-252
    • Caffarelli, L.1    Kohn, J.J.2    Nirenberg, L.3    Spruck, J.4
  • 8
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. Crandall, H. Ishi, and P.L. Lions User's guide to viscosity solutions of second order partial differential equations Bull. Amer. Math. Soc. 27 1 1992
    • (1992) Bull. Amer. Math. Soc. , vol.27 , Issue.1
    • Crandall, M.1    Ishi, H.2    Lions, P.L.3
  • 10
    • 0000559523 scopus 로고
    • On the Dirichlet problem for weakly non-linear elliptic partial differential equations
    • E.N. Dancer On the Dirichlet problem for weakly non-linear elliptic partial differential equations Proc. Roy. Soc. Edinburgh Sect. A 76 4 1976/77 283 300
    • (1976) Proc. Roy. Soc. Edinburgh Sect. A , vol.76 , Issue.4 , pp. 283-300
    • Dancer, E.N.1
  • 11
    • 0002413536 scopus 로고
    • p-2u′)′+f(t,u)=0, u(0)=u(T)=0,p>1
    • M. del Pino, M. Elgueta, and R. Manásevich A homotopic deformation along p of a Leray-Schauder degree result and existence for (| u ′ | p - 2 u ′) ′ + f (t, u) = 0, u (0) = u (T) = 0, p > 1 J. Differential Equations 80 1 1989 1 13
    • (1989) J. Differential Equations , vol.80 , Issue.1 , pp. 1-13
    • Del Pino, M.1    Elgueta, M.2    Manásevich, R.3
  • 12
    • 0000633180 scopus 로고
    • F. Global bifurcation from the eigenvalues of the p-Laplacian
    • M. del Pino, and R. Manásevich F. Global bifurcation from the eigenvalues of the p-Laplacian J. Differential Equations 92 2 1991 226 251
    • (1991) J. Differential Equations , vol.92 , Issue.2 , pp. 226-251
    • Del Pino, M.1    Manásevich, R.2
  • 13
    • 0003322299 scopus 로고
    • Solvability and Bifurcations of Nonlinear Equations
    • Longman Scientific and Technical Harlow
    • P. Drábek Solvability and Bifurcations of Nonlinear Equations Pitman Res. Notes Math. Ser. vol. 264 1992 Longman Scientific and Technical Harlow copublished in the United States with John Wiley and Sons, New York, 1992
    • (1992) Pitman Res. Notes Math. Ser. , vol.264
    • Drábek, P.1
  • 14
    • 0038729477 scopus 로고    scopus 로고
    • Critical exponents for the Pucci's extremal operators
    • P. Felmer, and A. Quaas Critical exponents for the Pucci's extremal operators C. R. Acad. Sci. Paris, Ser. I 335 2002 909 914
    • (2002) C. R. Acad. Sci. Paris, Ser. I , vol.335 , pp. 909-914
    • Felmer, P.1    Quaas, A.2
  • 15
    • 0346724409 scopus 로고    scopus 로고
    • On critical exponents for the Pucci's extremal operators
    • P. Felmer, and A. Quaas On critical exponents for the Pucci's extremal operators Ann Inst. H. Poicaré Anal. Non Linéaire 20 5 2003 843 865
    • (2003) Ann Inst. H. Poicaré Anal. Non Linéaire , vol.20 , Issue.5 , pp. 843-865
    • Felmer, P.1    Quaas, A.2
  • 16
    • 1942478381 scopus 로고    scopus 로고
    • Positive solutions to 'semilinear' equation involving the Pucci's operator
    • P. Felmer, and A. Quaas Positive solutions to 'semilinear' equation involving the Pucci's operator J. Differential Equations 199 2004 376 393
    • (2004) J. Differential Equations , vol.199 , pp. 376-393
    • Felmer, P.1    Quaas, A.2
  • 17
    • 84972531402 scopus 로고
    • On the first curve of the Fučik spectrum of an elliptic operator
    • D. de Figueiredo, and J.P. Gossez On the first curve of the Fučik spectrum of an elliptic operator Differential Integral Equations 7 5-6 1994 1285 1302
    • (1994) Differential Integral Equations , vol.7 , Issue.5-6 , pp. 1285-1302
    • De Figueiredo, D.1    Gossez, J.P.2
  • 18
    • 0003219003 scopus 로고
    • Solvability of Nonlinear Equations and Boundary Value Problems
    • Reidel
    • S. Fučík Solvability of Nonlinear Equations and Boundary Value Problems Math. Appl. vol. 4 1980 Reidel With a foreword by Jean Mawhin
    • (1980) Math. Appl. , vol.4
    • Fučík, S.1
  • 19
    • 0001719684 scopus 로고
    • Résultats d'existence et de non-existence pour certains problemes demi-linéaires a l'infini
    • T. Gallouet, and O. Kavian Résultats d'existence et de non-existence pour certains problemes demi-linéaires a l'infini (in French. English summary) Existence and nonexistence results for certain semilinear problems at infinity Ann. Fac. Sci. Toulouse Math. 5 3-4 1981 201 246
    • (1981) Ann. Fac. Sci. Toulouse Math. , vol.5 , Issue.3-4 , pp. 201-246
    • Gallouet, T.1    Kavian, O.2
  • 21
    • 0020703936 scopus 로고
    • Bifurcation and optimal stochastic control
    • P.L. Lions Bifurcation and optimal stochastic control Nonlinear Anal. 2 1983 177 207
    • (1983) Nonlinear Anal. , vol.2 , pp. 177-207
    • Lions, P.L.1
  • 22
    • 84947513018 scopus 로고
    • Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications
    • P.L. Lions Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications Comm. Partial Differential Equations 8 10 1983 1101 1174
    • (1983) Comm. Partial Differential Equations , vol.8 , Issue.10 , pp. 1101-1174
    • Lions, P.L.1
  • 23
    • 84953017099 scopus 로고
    • Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II. Viscosity solutions and uniqueness
    • P.L. Lions Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II. Viscosity solutions and uniqueness Comm. Partial Differential Equations 8 11 1983 1229 1276
    • (1983) Comm. Partial Differential Equations , vol.8 , Issue.11 , pp. 1229-1276
    • Lions, P.L.1
  • 25
    • 84966204935 scopus 로고
    • A remark on Bony maximum principle
    • P.L. Lions A remark on Bony maximum principle Proc. Amer. Math. Soc. 88 3 1983 503 508
    • (1983) Proc. Amer. Math. Soc. , vol.88 , Issue.3 , pp. 503-508
    • Lions, P.L.1
  • 26
    • 0011467268 scopus 로고
    • Two remarks on Monge-Ampère equations
    • P.L. Lions Two remarks on Monge-Ampère equations Ann. Mat. Pura Appl. 142 4 1985 263 275
    • (1985) Ann. Mat. Pura Appl. , vol.142 , Issue.4 , pp. 263-275
    • Lions, P.L.1
  • 27
    • 84990576581 scopus 로고
    • Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0
    • W.M. Ni, and R. Nussbaum Uniqueness and nonuniqueness for positive radial solutions of Δ u + f (u, r) = 0 Comm. Pure Appl. Math. 38 1985 67 108
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 67-108
    • Ni, W.M.1    Nussbaum, R.2
  • 28
    • 0000531454 scopus 로고
    • Operatori ellittici estremanti
    • C. Pucci Operatori ellittici estremanti Ann. Mat. Pure Appl. 72 1966 141 170
    • (1966) Ann. Mat. Pure Appl. , vol.72 , pp. 141-170
    • Pucci, C.1
  • 29
    • 0040450749 scopus 로고
    • Maximum and minimum first eigenvalue for a class of elliptic operators
    • C. Pucci Maximum and minimum first eigenvalue for a class of elliptic operators Proc. Amer. Math. Soc. 17 1966 788 795
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 788-795
    • Pucci, C.1
  • 30
    • 13844311974 scopus 로고    scopus 로고
    • Existence of positive solutions to a 'semilinear' equation involving the Pucci's operator in a convex domain
    • A. Quaas Existence of positive solutions to a 'semilinear' equation involving the Pucci's operator in a convex domain Differential Integral Equations 17 2004 481 494
    • (2004) Differential Integral Equations , vol.17 , pp. 481-494
    • Quaas, A.1
  • 31
    • 84879904964 scopus 로고
    • Some aspect of nonlinear eigenvalue problem
    • P.H. Rabinowitz Some aspect of nonlinear eigenvalue problem Rocky Moutain J. Math. 74 3 1973 161 202
    • (1973) Rocky Moutain J. Math. , vol.74 , Issue.3 , pp. 161-202
    • Rabinowitz, P.H.1
  • 32
    • 36448974335 scopus 로고
    • Some global results for nonlinear eigenvalue problems
    • P.H. Rabinowitz Some global results for nonlinear eigenvalue problems J. Funct. Anal. 7 1971 487 513
    • (1971) J. Funct. Anal. , vol.7 , pp. 487-513
    • Rabinowitz, P.H.1
  • 33
    • 0041384227 scopus 로고
    • Théorie du degré topologique et applications à des problèmes aux limites non linéaires
    • Numérique Université PARIS VI
    • P.H. Rabinowitz, Théorie du degré topologique et applications à des problèmes aux limites non linéaires, Lectures Notes Lab. Analyse Numérique Université PARIS VI, 1975
    • (1975) Lectures Notes Lab. Analyse
    • Rabinowitz, P.H.1
  • 35
    • 0009336331 scopus 로고
    • On the classical solution of Bellman elliptic equation
    • M.V. Safonov On the classical solution of Bellman elliptic equation Soviet Math. Dokl. 30 1984
    • (1984) Soviet Math. Dokl. , vol.30
    • Safonov, M.V.1
  • 36
    • 0001333452 scopus 로고
    • The Fučík spectrum
    • M. Schechter The Fučík spectrum Indiana Univ. Math. J. 43 4 1994 1139 1157
    • (1994) Indiana Univ. Math. J. , vol.43 , Issue.4 , pp. 1139-1157
    • Schechter, M.1


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