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Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type B p , q s and F p , q s

Jens Franke; Thomas Runst

Czechoslovak Mathematical Journal (1988)

  • Volume: 38, Issue: 4, page 623-641
  • ISSN: 0011-4642

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Franke, Jens, and Runst, Thomas. "Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s_{p,q}$ and $F^s_{p,q}$." Czechoslovak Mathematical Journal 38.4 (1988): 623-641. <http://eudml.org/doc/13737>.

@article{Franke1988,
author = {Franke, Jens, Runst, Thomas},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear perturbations; function spaces; Existence},
language = {eng},
number = {4},
pages = {623-641},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s_\{p,q\}$ and $F^s_\{p,q\}$},
url = {http://eudml.org/doc/13737},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Franke, Jens
AU - Runst, Thomas
TI - Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s_{p,q}$ and $F^s_{p,q}$
JO - Czechoslovak Mathematical Journal
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 4
SP - 623
EP - 641
LA - eng
KW - nonlinear perturbations; function spaces; Existence
UR - http://eudml.org/doc/13737
ER -

References

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  1. S. Agmon A. Douglis L. Nirenberg, 10.1002/cpa.3160120405, Comm. Pure Appl. Math. 12 (1959), 623-727. (1959) MR0125307DOI10.1002/cpa.3160120405
  2. J. Franke, Regular elliptic boundary value problems in Besov and Triebel-Lizorkin spaces. The case 0 < p ≤ ∞ , 0 < q ≤ ∞ , Math. Nachr. (to appear). MR1349041
  3. J. Franke, 10.1002/mana.19861250104, Math. Nachr. 125 (1986), 29-68. (1986) MR0847350DOI10.1002/mana.19861250104
  4. J. Franke T. Runst, 10.1007/BF01905928, Analysis Math. 13 (1987), 3-27. (1987) MR0893032DOI10.1007/BF01905928
  5. S. Fučík, Solvability of Nonlinear Equations and Boundary Value Problems, Soc. Czechoslovak Math. Phys., Prague 1980. (1980) MR0620638
  6. S. Fučík A. Kufner, Nonlinear Differential Equations, Elsevier, Amsterdam 1980. (1980) MR0558764
  7. P. Hess, 10.1512/iumj.1974.23.23068, Indiana Univ. Math. J. 23 (1974), 827-829. (1974) Zbl0259.35036MR0352687DOI10.1512/iumj.1974.23.23068
  8. V. Klee, 10.1007/BF01360763, Math. Ann. 141 (1960), 281 - 285. (1960) Zbl0096.08001MR0131150DOI10.1007/BF01360763
  9. E. M. Landesman A. C. Lazer, Nonlinear perturbation of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. (1970) MR0267269
  10. J. Nečas, Sur l'Alternative de Fredholm pour les opérateurs non-linéaires avec application aux problèmes aux limites, Ann. Scuola Norm. Sup. Pisa 23 (1969), 331 - 345. (1969) MR0267430
  11. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  12. J. Nečas, On the range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolinae 14 (1973), 63 - 72. (1973) MR0318995
  13. S. I. Pokhozhaev, The solvability of non-linear equations with odd operators, (Russian). Functionalnyi analys i prilož. 1 (1967), 66-73. (1967) 
  14. T. Riedrich, Vorlesungen über nichtlineare Operatorengleichungen, Teubner-Texte Math., Teubner, Leipzig, 1976. (1976) Zbl0332.47026MR0467414
  15. T. Runst, 10.1007/BF01909369, Analysis Math. 12(1986), 313-346. (1986) MR0877164DOI10.1007/BF01909369
  16. H. Triebel, Spaces of Besov-Hardy-Sobolev Type, Teubner-Texte Math., Teubner, Leipzig, 1978. (1978) Zbl0408.46024MR0581907
  17. H. Triebel, Theory of Function Spaces, Akademische Verlagsgesellschaft Geest & Portig, Lepzig, 1983, und Birkhäuser, Boston, 1983. (1983) Zbl0546.46028MR0781540
  18. H. Triebel, 10.1080/03605307808820088, Comm. Partial Differential Equations 3 (1978), 1083-1164. (1978) Zbl0403.35034MR0512083DOI10.1080/03605307808820088
  19. H. Triebel, Mapping properties of Non-linear Operators Generated by Φ ( u ) = | u | ρ and by Holomorphic Φ ( u ) in Function Spaces of Besov-Hardy-Sobolev Type. Boundary Value Problems for Elliptic Differential Equations of Type Δ u = f ( x ) + Φ ( u ) , Math. Nachr. 117 (1984), 193-213. (1984) MR0755303
  20. S. A. Williams, 10.1016/0022-0396(70)90031-8, J. Differential Equations 8 (1970), 580-586. (1970) Zbl0209.13003MR0267267DOI10.1016/0022-0396(70)90031-8
  21. E. Zeidler, Vorlesungen über nichtlineare Functionalanalysis II - Monotone Operatoren, - Teubner-Texte Math., Teubner, Leipzig, 1977. (1977) MR0473928

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