Solvability of semilinear equations with strong nonlinearities and applications to elliptic problems

References

• Agmon , S. 1962 . On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems . Comm. Pure App. Math , 15 : 119 – 147 .
   Web of Science ®Google Scholar
• Agmon , S. and Stanković , B. 1965 . Lectures on Elliptic Boundary Value Problems , Van Nostrand, NJ : Princeton .
   Google Scholar
• Bahri , A. and Coron , J.M. 1985 . Sur une équation elliptique nonlinéaire avec . C.R. Acad. Sc. Paris , 301 ( I ) : 345 – 348 .
   Google Scholar
• Bahri , A. and Lions , P.L. 1985 . Remarques sur la théorie variationnelle des points critiques et applications . C.R. Acad. Sc. Paris , 301 ( I ) : 145 – 147 .
   Google Scholar
• Brezis , H. and Browder , F.E. 1982 . Some properties of higher order Sobolev spaces . J. Math. Pures Appl , 61 ( I ) : 245 – 259 .
   Google Scholar
• Brezis , H. and Nirenberg , L. 1983 . Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents . Comm. Pure Appl. Math , 36 ( I ) : 437 – 477 .
   Google Scholar
• Browder , F.E. 1971 . Exsistence theory for boundary-value problems for quasi-linear elliptic systems with strongly nonlinear lower order terms . Proc. Symp. Pure Math , 23 ( I ) : 269 – 286 . AMS, Providence, 1973
   Google Scholar
• Browder , F.E. 1983 . Degree of mapping for nonlinear mappings of monotone type . Proc. Nat. Acad. Sci , 180 ( I ) : 2408 – 2409 .
   Google Scholar
• Hess , P. 1973 . On nonlinear mappings of monotone type with respect to two Banach spaces . J. Math. Pures Appl , 52 ( I ) : 13 – 16 .
   Google Scholar
• Kato , T. 1984 . Locally coercive nonlinear equations with applications to some periodic solutions . Duke Math. J , 51 ( I ) : 923 – 936 .
   Google Scholar
• Kesavan , S. 1983 . Existence of solutions by the Galerkin method for a class of nonlinear problems . Applicable Anal , 16 ( I ) : 279 – 290 .
   Google Scholar
• Landes , R. and Mustonen , V. 1985 . Boundary value problems of strongly nonlinear second order elliptic equations . Bollettino U.M.I. , 4-B ( 6 ) : 33 – 55 .
   Google Scholar
• Lions , P.L. 1982 . On the existence of positive solutions of semilinear elliptic equations . SI AM Review , 24 ( 6 ) : 441 – 467 .
   Google Scholar
• Milojević , P.S. 1985 . Solvability of some semilinear equations with strong nonlinearities-I . II Abstracts AMS , 85T ( 47 ) 01-10 : 16 – 264 .
   Google Scholar
• Moser , J. 1966 . A rapidly convergent iteration method and non-linear partial differential equations-I . Ann. Scouola Normale Supp. Pisa , 20 ( 47 ) 01-10 : 265 – 315 .
   Google Scholar
• Rabinowitz , P.H. 1984 . A rapid convergence method for a singular pertur-bation problem . Ann. Inst. Henri Poincaré, Analyse nonlinéaire , 1 ( 47 ) 01-10 : 1 – 17 .
   Google Scholar
• Webb , J.R.L. 1980 . Boundary value problems of strongly nonlinear elliptic equations . J. London Math. Soc , 21 ( 2 ) 01-10 : 123 – 132 .
   Google Scholar