| Title:
|
Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s_{p,q}$ and $F^s_{p,q}$ (English) |
| Author:
|
Franke, Jens |
| Author:
|
Runst, Thomas |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1988 |
| Pages:
|
623-641 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35J65 |
| MSC:
|
46E35 |
| MSC:
|
47H15 |
| idZBL:
|
Zbl 0676.35031 |
| idMR:
|
MR962907 |
| DOI:
|
10.21136/CMJ.1988.102259 |
| . |
| Date available:
|
2008-06-09T15:23:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102259 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Franke: Regular elliptic boundary value problems in Besov and Triebel-Lizorkin spaces. The case $0<p \leq \infty$, $0<q \leq \infty$.Math. Nachr. (to appear). MR 1349041 |
| Reference:
|
[3] J. Franke: On the spaces $F\sb {pq}\sp s$ of Triebel-Lizorkin type: Pointwise multipliers and spaces on domains.Math. Nachr. 125 (1986), 29-68. MR 0847350, 10.1002/mana.19861250104 |
| Reference:
|
[4] J. Franke T. Runst: On the admissibility of function spaces of type $B\sp s\sb {p,q}$ and $F\sp s\sb {p,q}$. Boundary value problems for non-linear partial differential equations.Analysis Math. 13 (1987), 3-27. MR 0893032, 10.1007/BF01905928 |
| Reference:
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| Reference:
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[6] S. Fučík A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam 1980. MR 0558764 |
| Reference:
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[7] P. Hess: On a theorem by Landesman and Lazer.Indiana Univ. Math. J. 23 (1974), 827-829. Zbl 0259.35036, MR 0352687, 10.1512/iumj.1974.23.23068 |
| Reference:
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[8] V. Klee: Leray-Schauder theory without local convexity.Math. Ann. 141 (1960), 281 - 285. Zbl 0096.08001, MR 0131150, 10.1007/BF01360763 |
| Reference:
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[9] E. M. Landesman A. C. Lazer: Nonlinear perturbation of linear elliptic boundary value problems at resonance.J. Math. Mech. 19 (1970), 609-623. MR 0267269 |
| Reference:
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[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. MR 0267430 |
| Reference:
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[11] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
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[ 12] J. Nečas: On the range of nonlinear operators with linear asymptotes which are not invertible.Comment. Math. Univ. Carolinae 14 (1973), 63 - 72. MR 0318995 |
| Reference:
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[13] S. I. Pokhozhaev: The solvability of non-linear equations with odd operators.(Russian). Functionalnyi analys i prilož. 1 (1967), 66-73. |
| Reference:
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[14] T. Riedrich: Vorlesungen über nichtlineare Operatorengleichungen.Teubner-Texte Math., Teubner, Leipzig, 1976. Zbl 0332.47026, MR 0467414 |
| Reference:
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[15] T. Runst: Mapping properties of non-linear operators in spaces of type $B\sp s\sb {p,q}$ and $F\sp s\sb {p,q}$.Analysis Math. 12(1986), 313-346. MR 0877164, 10.1007/BF01909369 |
| Reference:
|
[16] H. Triebel: Spaces of Besov-Hardy-Sobolev Type.Teubner-Texte Math., Teubner, Leipzig, 1978. Zbl 0408.46024, MR 0581907 |
| Reference:
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[17] H. Triebel: Theory of Function Spaces.Akademische Verlagsgesellschaft Geest & Portig, Lepzig, 1983, und Birkhäuser, Boston, 1983. Zbl 0546.46028, MR 0781540 |
| Reference:
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[18] H. Triebel: On Besov-Hardy-Sobolev Spaces in domains and regular elliptic boundary value problems. The case $0<p \leq \infty$.Comm. Partial Differential Equations 3 (1978), 1083-1164. Zbl 0403.35034, MR 0512083, 10.1080/03605307808820088 |
| Reference:
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[19] H. Triebel: Mapping properties of Non-linear Operators Generated by $\Phi (u)=\vert u\vert \sp{\rho }$ and by Holomorphic $\Phi (u)$ in Function Spaces of Besov-Hardy-Sobolev Type. Boundary Value Problems for Elliptic Differential Equations of Type $\Delta u=f(x)+\Phi (u)$.Math. Nachr. 117 (1984), 193-213. MR 0755303 |
| Reference:
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[20] S. A. Williams: A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem.J. Differential Equations 8 (1970), 580-586. Zbl 0209.13003, MR 0267267, 10.1016/0022-0396(70)90031-8 |
| Reference:
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[21] E. Zeidler: Vorlesungen über nichtlineare Functionalanalysis II - Monotone Operatoren.- Teubner-Texte Math., Teubner, Leipzig, 1977. MR 0473928 |
| . |
