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Integral Transforms and Special Functions Volume 20, 2009 - Issue 3-4: PROCEEDINGS OF THE CONFERENCE: LINEAR AND NON-LINEAR THEORY OF GENERALIZED FUNCTIONS AND ITS APPLICATIONS, HELD IN BEDLEWO, POLAND, 2–8 SEPTEMBER 2007
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Original Articles

Spaces of anisotropic ultradifferentiable functions and local solvability for semilinear partial differential equations

Lucio Cadeddu Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy
&
Todor Gramchev Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, ItalyCorrespondence[email protected]
Pages 275-282 | Received 22 Apr 2008, Published online: 01 Dec 2010

References

  • Albanese , A. and Bonet , J. 2007 . Ultradifferentiable fundamental kernels of linear partial differential operators on non-quasianalytic classes of Roumieu type . Publ. Res. Inst. Math. Sci. , 43 : 39 – 54 .
  • Cadeddu , L. and Gramchev , T. 2006 . Scales of Banach spaces in inhomogeneous Gevrey classes . C. R. Acad. Bulgare Sci. , 59 : 903 – 910 .
  • Calvo , D. , Morando , A. and Rodino , L. 2004 . Inhomogeneous Gevrey classes and ultradistributions . J. Math. Anal. Appl. , 297 : 720 – 739 .
  • DeDonno , G. and Oliaro , A. 2003 . Local solvability and hypoellipticity for semilinear anisotropic partial differential equations . Trans. Amer. Math. Soc. , 355 : 3405 – 3432 .
  • DeDonno , G. and Oliaro , A. 2006 . Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity . Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. , : 583 – 610 . (8)9 3
  • Djakov , P. and Mityagin , B. 2002 . Smoothness of solutions of nonlinear ODE . Math. Ann. , 324 : 225 – 254 .
  • Eida , A. and Pilipović , S. 2005 . Composition of ultradistributions and corresponding microfunctions with ℰ*-functions . Rocky Mountain J. Math. , 35 : 137 – 147 .
  • Gourdin , D. and Gramchev , T. 2007 . Global in time solutions of evolution equations in scales of Banach function spaces in ℝ n . Bull. Sci. Math. , 131 : 761 – 786 .
  • Komatsu , H. 1979 . The implicit function theorem for ultradifferentiable mappings . Proc. Japan Acad., Ser. A , 55 : 69 – 72 .
  • Liess , O. and Rodino , L. 1984 . Inhomogeneous Gevrey classes and related pseudodifferential operators . Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. , 3 : 233 – 323 .
  • Marco , J.-P. and Sauzin , D. 2002 . Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems . Publ. Math. Inst. Hautes Etudes Sci. , 96 : 199 – 275 .
  • Oliaro , A. 2007 . Local solvability for powers of anisotropic operators . Appl. Anal. , 86 : 421 – 431 .
  • Oliaro , A. , Popivanov , P. and Rodino , L. 2004 . “ Local solvability for partial differential equations with multiple characteristics ” . In Abstract and Applied Analysis , 257 – 270 . River Edge, NJ : World Sci. Publ .
  • Popov , G. 2000 . Invariant tori, effective stability, and quasimodes with exponentially small error terms. I. Birkoff normal forms . Ann. Henri Poincaré , 1 : 223 – 248 .
  • Rodino , L. 1993 . Linear Partial Differential Operators in Gevrey Spaces , River Edge, NJ : World Scientific Publishing Co., Inc .
  • Roumieu , C. 1962 . Ultra-distributions definies sur Rn et sur certaines classes de variétés différentiables . J. Anal. Math. , 10 : 153 – 192 .

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