A combined variational–monotone iterative method for elliptic boundary value problems with discontinuous nonlinearity

References

• Amann , H. Order structures and fixed points, Mathematisches Institut , Ruhr-Universitamp;t Bochum .
   Google Scholar
• Ambrosetti , A. and Turner , R.E.L. 1988 . Some discontinuous variational problems . Differential Integral Equations , 1 : 341 – 349 .
   Google Scholar
• Ambrosetti , A. and Badiale , M. 1989 . The dual variational principle and elliptic problems with discontinuous nonlinearities . J. Math. Anal , 140 : 363 – 373 .
   Google Scholar
• Aris , R. 1975 . The mathematical theory of diffusion and reaction , Oxford : Clarendon Press .
   Google Scholar
• Barbu , V. and Th. Precupanu . 1978 . Convexity and optimization in Banach spaces , Bucuresti and Sijthoff Noordhoff : Editura Academici .
   Google Scholar
• Benilan , P. , Crandall , M. G. and Sacks , P. 1988 . Some L existence and dependence results for semilinear el¬liptic equations under nonlinear boundary conditions . Appl. Math. Optim , 7 : 203 – 224 .
   Google Scholar
• Brezis , H. 1972 . Integrals convexes dans les espaces de Sobolev . Israel J. Math , 13 : 9 – 23 .
   Web of Science ®Google Scholar
• Carl , S. 1988 . Ein konstruktiver Existenzsatz fiir Randwert-probierne elliptischer Differentialgleichungen zweiter Ordnung mit unstetiger Nichtlinearit&t . Math. Nachr , 138 : 55 – 65 .
   Web of Science ®Google Scholar
• Carl , S. 1989 . The monotone iterative technique for a para¬bolic boundary value problem with discontinuous non-linearity . Nonlinear Anal , 13 : 1399 – 1407 .
   Google Scholar
• Chandra , J. and Fleishman , B. A. 1974 . Existence and compa¬rison results for a class of nonlinear boundary value problems . Ann, Math, pura appl , 101 : 247 – 261 .
   Google Scholar
• Chang , K.C. 1980 . The obstacle problem and partial diffe¬rential equations with discontinuous nonlinearities . Commun. Pure Appl. Math , 33 : 117 – 146 .
   Web of Science ®Google Scholar
• Davis , P.W. and Fleishman , B. A. 1986 . A discontinuous non¬linear problem: stability and convergence of iterates in a finite number of steps . Appl. Anal , 23 : 139 – 157 .
   Google Scholar
• Diaz , J.I. 1985 . Nonlinear partial differential equations and free boundaries I; elliptic equations . Res. Notes Math , 106
   Google Scholar
• Diaz , J.I. and Hernandez , J. 1984 . On the existence of a free boundary for a class of reaction-diffusion systems . SIAM J. Math. Anal , 15 : 670 – 685 .
   Web of Science ®Google Scholar
• Duvallet , A. 1989 . A theorem of existence for discontinuous differential systems with two point boundary condi¬tions . Nonlinear Anal , 13 : 43 – 51 .
   Google Scholar
• Gilbarg , D. and Trudinger , N. S. 1983 . Elliptic partial differential equations of second order , Springer-Verlag : Berlin/Heidelberg .
   Google Scholar
• HeikkilE , S. 1983 . On an elliptic boundary value problem with discontinuous nonlinearity . Differential Integral Equations ,
   Google Scholar
• HeikkilE , S. , Lakshmikantham , V. and Leela , S. 1988 . Applications of monotone techniques to differential equations with discontinuous right-hand side . Differential Integral Equations , 1 : 287 – 297 .
   Google Scholar
• Keady , G. and Kloeden , P. E. 1987 . An elliptic boundary-value problem with a discontinuous nonlinearity II . Proc. Roy. Soc. Edinburgh , 105 : 23 – 36 .
   Google Scholar
• Naumann , J. 1987 . Einftihrung in die Theorie parabolischer Variationsungleichungen . BSB B. G. Teubner Verlags-gesellschaft , 105
   Google Scholar
• Norbury , J. and Stuart , A. M. 1987 . Parabolic free boundary problems arising in porous medium combustion . IMA J. Appl. Math , 39 : 241 – 257 .
   Google Scholar
• Panagiotopoulos , P.D. 1985 . Inequality problems in me¬chanics and applications , Boston/Basel/ Stuttgart : Birkhauser .
   Google Scholar
• Stuart , C.A. 1978 . Maximal and minimal solutions of ellip¬tic differential equations with discontinuous nonli-nearities . Math. Z , 163 : 239 – 249 .
   Google Scholar
• Wloka , J. 1982 . Partielle Differentialgleichungen , Leipzig : BSB B. G. Teubner Verlagsgesellschaft .
   Google Scholar
• Zeidler , E. 1985 . Nonlinear functional analysis and its applications III, - Variational methods , New York : Springer-Verlag .
   Google Scholar