메뉴 건너뛰기




Volumn 37, Issue 6, 1999, Pages 1751-1766

Nonconvex variational problems related to a hyperbolic equation

Author keywords

[No Author keywords available]

Indexed keywords

BANG BANG CONTROL SYSTEMS; BOUNDARY CONDITIONS; LYAPUNOV METHODS; PROBLEM SOLVING; THEOREM PROVING; VARIATIONAL TECHNIQUES;

EID: 0033184484     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012998332299     Document Type: Article
Times cited : (11)

References (28)
  • 1
    • 0028481339 scopus 로고
    • On passing to the limit for non convex variational problems
    • M. AMAR AND A. CELLINA, On passing to the limit for non convex variational problems, Asymptot. Anal., 9 (1994), pp. 135-148.
    • (1994) Asymptot. Anal. , vol.9 , pp. 135-148
    • Amar, M.1    Cellina, A.2
  • 2
    • 85011845668 scopus 로고
    • A nonconvex variational problem with constraints
    • M. AMAR AND C. MARICONDA, A nonconvex variational problem with constraints, SIAM J. Control Optim., 33 (1995), pp. 299-307.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 299-307
    • Amar, M.1    Mariconda, C.2
  • 3
    • 84956096521 scopus 로고
    • Convexity of values of vectors integrals, theorems on measurable choice and variational problems
    • V. I. ARKIN AND V. L. LEVIN, Convexity of values of vectors integrals, theorems on measurable choice and variational problems, Russian Math. Surveys, 27 (1972), pp. 21-85.
    • (1972) Russian Math. Surveys , vol.27 , pp. 21-85
    • Arkin, V.I.1    Levin, V.L.2
  • 4
    • 0000245772 scopus 로고
    • On a variational problem
    • Z. ARTSTEIN, On a variational problem, J. Math. Anal. Appl., 45 (1974), pp. 404-415.
    • (1974) J. Math. Anal. Appl. , vol.45 , pp. 404-415
    • Artstein, Z.1
  • 6
    • 0343045892 scopus 로고
    • A multidimensional lyapunov type theorem
    • A. BRESSAN, A multidimensional Lyapunov type theorem, Studia Math., 106 (1993), pp. 121-128.
    • (1993) Studia Math. , vol.106 , pp. 121-128
    • Bressan, A.1
  • 7
    • 0007081394 scopus 로고
    • Multivariable aumann integral and controlled wave equations
    • A. BRESSAN AND F. FLORES-BAZÁN, Multivariable Aumann integral and controlled wave equations, J. Math. Anal. Appl., 189 (1995), pp. 315-334
    • (1995) J. Math. Anal. Appl. , vol.189 , pp. 315-334
    • Bressan, A.1    Flores-Bazán, F.2
  • 8
    • 33746962715 scopus 로고
    • On a classical problem of the calculus of variations without convexity assumptions
    • A. CELLINA AND G. COLOMBO, On a classical problem of the calculus of variations without convexity assumptions, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), pp. 97-106.
    • (1990) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.7 , pp. 97-106
    • Cellina, A.1    Colombo, G.2
  • 9
    • 85013215127 scopus 로고
    • Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions
    • A. CELLINA AND F. FLORES-BAZÁN, Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions, Ann. Inst. H. Poincaré Anal. Non Linéaire, 9 (1992), pp. 465-478.
    • (1992) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.9 , pp. 465-478
    • Cellina, A.1    Flores-Bazán, F.2
  • 11
    • 0030151550 scopus 로고    scopus 로고
    • An existence result for noncoercive nonconvex problems in the calculus of variations
    • G. CRASTA, An existence result for noncoercive nonconvex problems in the calculus of variations, Nonlinear Anal., 26 (1996), pp. 1527-1533.
    • (1996) Nonlinear Anal. , vol.26 , pp. 1527-1533
    • Crasta, G.1
  • 12
    • 0030284774 scopus 로고    scopus 로고
    • Existence results for noncoercive variational problems
    • G. CRASTA AND A. MALUSA, Existence results for noncoercive variational problems, SIAM J. Control Optim., 34 (1996), pp. 2064-2076.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 2064-2076
    • Crasta, G.1    Malusa, A.2
  • 14
    • 0342611748 scopus 로고    scopus 로고
    • On radial solutions to nonconvex variational problems
    • F. FLORES-BAZÁN, On radial solutions to nonconvex variational problems, Houston J. Math., 22 (1996), pp. 161-181.
    • (1996) Houston J. Math. , vol.22 , pp. 161-181
    • Flores-Bazán, F.1
  • 15
    • 4243274958 scopus 로고    scopus 로고
    • Optimal solutions in an allocation process for a continuum of traders
    • Technical Report 98-08, D.I.M., Universidad de Concepción, Concepción, Chile, to appear
    • F. FLORES-BAZÁN, Optimal Solutions in an Allocation process for a Continuum of Traders, Technical Report 98-08, D.I.M., Universidad de Concepción, Concepción, Chile, 1998; J. Global Optim., to appear.
    • (1998) J. Global Optim.
    • Flores-Bazán, F.1
  • 17
    • 84924362904 scopus 로고
    • Nonconvex integrals of the calculus of variations
    • Springer, New York
    • P. MARCELLINI, Nonconvex integrals of the calculus of variations, in Methods of Nonconvex Analysis, Lectures Notes in Math. 1446, Springer, New York, 1990, pp. 16-57.
    • (1990) Methods of Nonconvex Analysis, Lectures Notes in Math. , vol.1446 , pp. 16-57
    • Marcellini, P.1
  • 18
    • 38249010750 scopus 로고
    • On a parametric problem of the calculus of variations without convexity assumptions
    • C. MARICONDA, On a parametric problem of the calculus of variations without convexity assumptions, J. Math. Anal. Appl., 170 (1992), pp. 291-297.
    • (1992) J. Math. Anal. Appl. , vol.170 , pp. 291-297
    • Mariconda, C.1
  • 19
    • 0010681281 scopus 로고
    • The existence of optimal controls in the absence of convexity conditions
    • L. W. NEUSTADT, The existence of optimal controls in the absence of convexity conditions, J. Math. Anal. Appl., 7 (1963), pp. 110-117.
    • (1963) J. Math. Anal. Appl. , vol.7 , pp. 110-117
    • Neustadt, L.W.1
  • 20
    • 0011691505 scopus 로고
    • The Lyapunov theorem: Its extensions and applications
    • Springer, NY
    • C. OLECH, The Lyapunov theorem: its extensions and applications, in Methods of Non-convex Analysis, Lectures Notes in Math. 1446, Springer, NY, 1990, pp. 84-103.
    • (1990) Methods of Non-convex Analysis, Lectures Notes in Math. , vol.1446 , pp. 84-103
    • Olech, C.1
  • 21
    • 0015018113 scopus 로고
    • Existence theorems for an optimal control problem relative to a linear, hyperbolic partial differential equation
    • G. PULVIRENTI, Existence theorems for an optimal control problem relative to a linear, hyperbolic partial differential equation, J. Optim. Theory Appl., 7 (1971), pp. 109-117.
    • (1971) J. Optim. Theory Appl. , vol.7 , pp. 109-117
    • Pulvirenti, G.1
  • 22
    • 0025495824 scopus 로고
    • Existence theorems in optimal control problems without convexity assumptions
    • J. P. RAYMOND, Existence theorems in optimal control problems without convexity assumptions, J. Optim. Theory Appl., 67 (1990), pp. 109-132.
    • (1990) J. Optim. Theory Appl. , vol.67 , pp. 109-132
    • Raymond, J.P.1
  • 23
    • 0007137776 scopus 로고
    • Existence theorems without convexity assumptions for optimal control problems governed by parabolic and elliptic systems
    • J. P. RAYMOND, Existence theorems without convexity assumptions for optimal control problems governed by parabolic and elliptic systems, Appl. Math. Optim., 26 (1992), pp. 39-62.
    • (1992) Appl. Math. Optim. , vol.26 , pp. 39-62
    • Raymond, J.P.1
  • 25
    • 0343917463 scopus 로고
    • Existence and bang-bang theorems for control problems governed by hyperbolic equations
    • Calculus of Variations, Homogenization and Continuum Mechanics, World Scientific, River Edge, N.J.
    • J. P. RAYMOND, Existence and Bang-Bang Theorems for Control Problems Governed by Hyperbolic Equations, in Calculus of Variations, Homogenization and Continuum Mechanics, Ser. Adv. Math. Appl. Sci. 18, World Scientific, River Edge, N.J., 1993.
    • (1993) Ser. Adv. Math. Appl. Sci. , vol.18
    • Raymond, J.P.1
  • 26
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton NJ, 1972.
    • (1972) Convex Analysis
    • Rockafellar, R.T.1
  • 27
    • 0016951640 scopus 로고
    • Existence theorems for optimization problems concerning linear, hyperbolic partial differential equations without convexity conditions
    • M. B. SURYANARAYANA, Existence theorems for optimization problems concerning linear, hyperbolic partial differential equations without convexity conditions, J. Optim. Theory Appl., 19 (1976), pp. 47-61.
    • (1976) J. Optim. Theory Appl. , vol.19 , pp. 47-61
    • Suryanarayana, M.B.1
  • 28
    • 84972506711 scopus 로고
    • A Sobolev space and a Darboux problem
    • M. B. SURYANARAYANA, A Sobolev space and a Darboux problem, Pacific J. Math., 69 (1977), pp. 535-550.
    • (1977) Pacific J. Math. , vol.69 , pp. 535-550
    • Suryanarayana, M.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.