Publication Cover
Applicable Analysis
An International Journal
Volume 26, 1987 - Issue 1
20
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

On the development of functionals which satisfy a maximum principle

&
Pages 45-60 | Published online: 02 May 2007

References

  • Alikakos , N. 1981 . Remarks on invariance in reaction-diffusion equations . Nonlinear Analysis T. M.A , 5 : 593 – 614 .
  • Alikakos , N. 1983 . Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems . Proc. Royal Soc. Edinburgh , 94 ( A ) : 265 – 286 .
  • Bates , P. 1985 . Containment for weakly coupled parabolic systems . Houston J. of Math , 11 ( A ) : 151 – 158 .
  • Bebernes , J. and Schmitt , K. 1977 . Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations . Rocky Mountain J. of Math , 7 ( A ) : 557 – 567 .
  • Bell , J. and Cosner , C. 1981 . Stability properties of a model of parallel nerve fibers . J. Differential Equations , 40 ( A ) : 303 – 315 .
  • Cesari , L. 1971 . Asymptotic behavior and stability problems in ordinary differential equations , New York : Springer - Verlag .
  • Chow , S.N. and Dunninger , D.R. 1974 . A maximum principle for n-metaharmonic functions . Proc. A.M.S , 43 : 79 – 83 .
  • Chueh , K. , Conley , C. and Smoller , J. 1977 . positively invariant regions for systems of nonlinear diffusion equations . Indiana U. Math. J , 26 : 373 – 392 .
  • Cosner , C. 1981 . Pointwise a priori bounds for strongly coupled semilinear systems of parabolic partial differential equations . Indiana U. Math. J , 30 : 607 – 620 .
  • Dunninger , D.R. 1972 . Maximum principles for some fourth order elliptic equations . J. Math. Anal. Appl , 37 : 655 – 658 .
  • Goyal , V. B. and Schaefer , P.W. 1981 . On a subharmonic functional in fourth order nonlinear elliptic problems . J. Math. Anal. Appl , 83 : 20 – 25 .
  • Goyal , V.B. and Schaefer , P.W. 1982 . Liouville theorems for elliptic systems and nonlinear equations of fourth order . Proc. Royal Soc. Edinburgh , 91 ( A ) : 235 – 242 .
  • Goyal , V.B. and Schaefer , P.W. 1982 . Comparison principles for some fourth order elliptic problems . Lecture Notes in Mathematics , 964 : 272 – 279 .
  • Henry , D. 1981 . Geometric theory of semilinear parabolic equations . Lecture Notes in Mathematics , 840 : 1 – 348 .
  • Hile , G.N. and Protter , M.H. 1983 . Gradient bounds for weakly coupled nonlinear elliptic systems . Appl. Anal , 16 ( A ) : 51 – 70 .
  • Miranda , C. 1948 . Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche di due variabli . Gion. Mat. Battaglini , 78 ( A ) : 97 – 118 .
  • Miranda , C. 1970 . Sul teorema del massimo modulo per una classe di sistemi ellit-tici di equazioni del secondo ordine e per le equazioni a coefficienti complessi . Istituto Lombardo Accad. Sci. Lett. Rend , 104 ( A ) : 736 – 745 .
  • Nichols , E.C. 1986 . “ Maximum principles for P-functions in elliptic differential equations ” . In Ph.D. Dissertation , Knoxville, Tennessee : University of Tennessee .
  • Nicolaenko , B. , Scheurer , B. and Temam , R. 1985 . Some global dynamical problems of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors . Physica , 16 ( D ) : 155 – 183 .
  • Oleinik , O.A. and Radkevic , E.V. 1973 . Second order equations with nonnegative characteristic form , New York : Plenum Press .
  • Payne , L.E. 1976 . Some remarks on maximum principles . J. Analyse Math , 30 : 421 – 433 .
  • Protter , M.H. and Weinberger , H.F. 1967 . Maximum principles in differential equations , New Jersey : Prentice-Hall, Inc., Englewood Cliffs .
  • Protter , M.H. and Weinberger , H.F. 1973 . A maximum principle and gradient bounds for linear elliptic equations . Indiana U. Math. J , 23 : 239 – 249 .
  • Redheffer , R. and Walter , W. 1978 . Invariant sets for systems of partial differential equations I. parabolic equations . Arch. Rational Mech. Anal , 67 : 42 – 52 .
  • Redheffer , R. and Walter , W. 1980 . Invariant sets for systems of partial differential equations II. first order and elliptic equations . Arch. Rational Mech. Anal , 73 : 19 – 29 .
  • Schaefer , P.W. 1987 . Solution, gradient, and Laplacian bounds in some nonlinear fourth order elliptic equations . SIAM J. Math. Anal , 18 : 430 – 434 .
  • Serrin , J. 1977 . Liouville theorems and gradient bounds for quasilinear elliptic systems . Arch. Rational Mech. Anal , 66 : 295 – 310 .
  • Sperb , R.P. 1981 . Maximum principles and their applications , New York : Academic Press .
  • Walter , W. 1970 . Differential and integral inequalities , New York : Springer-Verlag .
  • Weinberger , H.F. 1975 . Invariant sets for weakly coupled parabolic and elliptic systems . Rendiconti di Matematica , 8 ( VI ) : 295 – 310 .
  • Yoshizawa , T. 1966 . Stability theory by Lyapunov's second method , 8 ( VI ) The Math. Soc. of Japan , Tokyo

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.