Monotone iterative scheme for nonlinear hyperbolic boundary value problem

References

• Aziz , A.K. and Diaz , K. 1962 . on a mixed boundary value problem for linear hyperbolic differential equations in two independent variables . Arch. Rat. Mech. Anal , 10 : 1 – 28 .
   Google Scholar
• Aziz , A.K. and Maloney , J.P. 1965 . An application by Tychonoff's fixed point theorem to hyperbolic partial differential equations . Math, Ann , 162 : 77 – 82 .
   Google Scholar
• Cesari , L. 1965 . Existence in the large of periodic solutions of hyperbolic partial differential equations . Arch. Rat. Mech. Anal , 20 : 170 – 190 .
   Google Scholar
• Cesari , L. and Kannan , R. 1979 . Existence of solutions of non-linear hyperbolic equations . Annali Scoula Normale Superiore-Pisa , 6 ( 47 ) : 573 – 592 .
   Google Scholar
• Cesari , L. and Kannan , R. 1982 . Solutions of Non-linear hyperbolic equations at resonance . Non linear analysis , 6 ( 47 ) : 751 – 805 .
   Google Scholar
• Chandra , J. and Davis , P.W. 1974 . A monotone method for quasi linear boundary value problems . Arch. Mat. Mech. Anal , 54 ( 47 ) : 357 – 366 .
   Google Scholar
• Chandra , J. , Lakshmikanthan , V. and Leela , S. 1978 . A monotone method for infinite systems of nonlinear boundary value problems . Arch. Rat. Mech. Anal , 68 ( 47 ) : 179 – 190 .
   Google Scholar
• Chandra , J. , Norman , P. and Dressel , F. 1981 . A monotone method for a system of non* linear parabolic differential equation . Proc. Royal Soc., Edinbourgh , 87A ( 47 ) : 209 – 217 .
   Google Scholar
• Conlan , J. 1959 . The Cauchy problem and the mixed boundary value problem for a non linear hyperbolic partial differential equation in two independent variables . Arch. Rat. Mech. Anal , 3 ( 47 ) : 355 – 380 .
   Google Scholar
• Du , S.W. and Lakshmikantham , V. 1982 . Monotone iterative technique for differential equations in Banach spaces . J. Math. Anal. Appl , 87 ( 47 ) : 454 – 459 .
   Google Scholar
• Ladde , G.S. , Lakshmikantham , V. and Pachpathe , B.G. 1982 . The method of upper, lower solutions and Volterra integral equations . J. Integral Equations , 87 ( 47 )
   Google Scholar
• Ladde , G.S. and Pachpathe , B.G. 1982 . Existence theorems for functional differential systems . J. Math. Anal. Appl , 90 ( 47 ) : 381 – 392 .
   Google Scholar
• Lakshmikantham , V. and Leela , S. 1969 . Differential and Integral Inequalities , New York : Academic Press .
   Google Scholar
• Lakshmikantham , V. and Leela , S. “ Oguztoreli, Quazi-solutions, Vector Lyapunov functions and monotone method ” . In IEEE Trans. Auto Control 1149 – 1153 .
   Google Scholar
• Lakshmikantham , V. , Leela , S and Vatsala , A.S . 1982 . Method of quazi-upper and lower solutions in abstract cones . Non linear Analaysis , 6 : 833 – 838 .
   Google Scholar
• Lakshmikantham , V. and Pachpathe , B.G. 1981 . Monotone method for non linear boundary value problems in transport process . Appl. Math. and Comp , 6 : 35 – 41 .
   Google Scholar
• Lakshmikantham , V. and Vatsala , A.S. 1981 . Quasi-solutions and monotone method for systems of non linear boundary value problems . J.Math. Anal. Appl , 79 : 38 – 41 .
   Google Scholar
• Lakshmikantham , V. and Vatsala , A.S. 1981 . Stability results for systems of reation diffusion systems by the method of quazi-solutions . Applicable Analysis , 12 : 229 – 235 .
   Web of Science ®Google Scholar
• Leela , S . 1983 . Monotone method for second order periodic boundary va;ue problems . Non linear Analysis , 7 : 349 – 355 .
   Google Scholar
• Walter , W. 1961 . Fehlerabschatzungen bei hyperbolischen differential gleichungen . Arch. Ratr Mech. Anal , 7 : 249 – 272 .
   Google Scholar