Spectral Theory for Linear Operators of Mixed Type and Applications to Nonlinear Dirichlet Problems

References

• Chang , C.C. ( 1989 ). On A Weighted Eigenvalue Problem of Equations of Mixed Type . Series in Pure Mathematics , Vol. 2 . Teaneck , NJ : World Scientific .
   Google Scholar
• de Figuieredo , D.G. ( 1982 ). Positive Solutions of Semilinear Elliptic Problems . Lecture Notes in Mathematics , Vol. 957 . Berlin-New York : Springer Verlag .
   Google Scholar
• Didenko , V.P. ( 1973 ). On the generalized solvability of the Tricomi problem . Ukrain. Math. J. 25 : 10 – 18 .
   Google Scholar
• Franchi , B. , Lanconelli , E. ( 1984 ). An embedding theorem for Sobolev spaces related to nonsmooth vector fields and Harnack inequality . Comm. Part. Diff. Eqs. 9 : 1237 – 1264 .
   Web of Science ®Google Scholar
• Han , Q. , Hong , J.-X. ( 2006 ). Isometric Embedding of Riemannian Manifolds in Euclidean Spaces . Mathematical Surveys and Monographs , Vol. 130 . Providence , RI : American Mathematical Society .
   Google Scholar
• Krasnosel'skii , M. ( 1964 ). Topological Methods in the Theory of Nonlinear Integral Equations . New York : The Macmillan Co .
   Google Scholar
• Lax , P. ( 1955 ). On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations . Comm. Pure Appl. Math. 8 : 615 – 633 .
   Web of Science ®Google Scholar
• Lupo , D. , Morawetz , C.S. , Payne , K.R. ( 2007 ). On closed boundary value problems for equations of mixed elliptic-hyperbolic type . Comm. Pure Appl. Math. 60 : 1319 – 1348 .
   Web of Science ®Google Scholar
• Lupo , D. , Payne , K.R. ( 2000 ). Existence of a principal eigenvalue for the Tricomi problem . Electron. J. Differ. Equ. Conf. 5 : 173 – 180 .
   Google Scholar
• Lupo , D. , Payne , K.R. ( 2000 ). On the maximum principle for generalized solutions to the Tricomi problem . Commun. Contemp. Math. 2 : 535 – 557 .
   Web of Science ®Google Scholar
• Lupo , D. , Payne , K.R. ( 2002 ). Spectral bounds for Tricomi problems and application to semilinear existence and existence with uniqueness results . J. Diff. Eqs. 184 : 139 – 162 .
   Web of Science ®Google Scholar
• Lupo , D. , Payne , K.R. ( 2003 ). Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types . Comm. Pure Appl. Math. 56 : 403 – 424 .
   Web of Science ®Google Scholar
• Lupo , D. , Payne , K.R. , Popivanov , N.I. (2005). Nonexistence of Nontrivial Solutions for Supercritical Equations of Mixed Elliptic-Hyperbolic Type . Progress in Nonlinear Differential Equations and Their Applications, Vol. 66 . Basel : Birkhäuser Verlag.
   Google Scholar
• Marino , A. ( 1973 ). La biforcazione nel caso variazionale . Confer. Sem. Mat. Univ. Bari 132 : 1 – 14 .
   Google Scholar
• Monticelli , D.D. , Payne , K.R. ( 2009 ). Maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction . J. Diff. Eqs. 247 : 1993 – 2026 .
   Web of Science ®Google Scholar
• Morawetz , C.S. ( 2004 ). Mixed equations and transonic flow . J. Hyper. Diff. Equ. 1 : 1 – 26 .
   Web of Science ®Google Scholar
• Ponomarev , S.M. ( 1980 ). On an eigenvalue problem for an equation of mixed type . Dokl. Akad. Nauk SSSR 251 : 1070 – 1072 .
   Google Scholar
• Rabinowitz , P.H. ( 1986 ). Minimax Methods in Critical Point Theory with Applications to Differential Equations . CBMS Regional Confererence Series in Mathematics , Vol. 65 . Providence , RI : American Mathematical Society .
   Google Scholar
• Vainberg , M.M. ( 1964 ). it Variational Methods for the Study of Nonlinear Operators . San Francisco : Holden-Day, Inc .
   Google Scholar