Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s_{p,q}$ and $F^s_{p,q}$
Franke, Jens ; Runst, Thomas
Czechoslovak Mathematical Journal, Tome 38 (1988), p. 623-641 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1988-01-01
Classification:  35J65,  46E35,  47H15 
@article{102259,
     author = {Jens Franke and Thomas Runst},
     title = {Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B^s\_{p,q}$ and $F^s\_{p,q}$},
     journal = {Czechoslovak Mathematical Journal},
     volume = {38},
     year = {1988},
     pages = {623-641},
     zbl = {0676.35031},
     mrnumber = {962907},
     language = {en},
     url = {http://dml.mathdoc.fr/item/102259}
}

Franke, Jens; 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, Tome 38 (1988) pp. 623-641. http://gdmltest.u-ga.fr/item/102259/

S. Agmon A. Douglis L. Nirenberg Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727. (1959) | Article | MR 0125307

J. Franke Regular elliptic boundary value problems in Besov and Triebel-Lizorkin spaces. The case $0

, Math. Nachr. (to appear). | MR 1349041

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. (1986) | MR 0847350

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. (1987) | Article | MR 0893032

S. Fučík Solvability of Nonlinear Equations and Boundary Value Problems, Soc. Czechoslovak Math. Phys., Prague 1980. (1980) | MR 0620638

S. Fučík A. Kufner Nonlinear Differential Equations, Elsevier, Amsterdam 1980. (1980) | MR 0558764

P. Hess On a theorem by Landesman and Lazer, Indiana Univ. Math. J. 23 (1974), 827-829. (1974) | Article | MR 0352687 | Zbl 0259.35036

V. Klee Leray-Schauder theory without local convexity, Math. Ann. 141 (1960), 281 - 285. (1960) | Article | MR 0131150 | Zbl 0096.08001

E. M. Landesman A. C. Lazer Nonlinear perturbation of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. (1970) | MR 0267269

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) | MR 0267430

J. Nečas Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) | MR 0227584

J. Nečas On the range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolinae 14 (1973), 63 - 72. (1973) | MR 0318995

S. I. Pokhozhaev The solvability of non-linear equations with odd operators, (Russian). Functionalnyi analys i prilož. 1 (1967), 66-73. (1967)

T. Riedrich Vorlesungen über nichtlineare Operatorengleichungen, Teubner-Texte Math., Teubner, Leipzig, 1976. (1976) | MR 0467414 | Zbl 0332.47026

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. (1986) | Article | MR 0877164

H. Triebel Spaces of Besov-Hardy-Sobolev Type, Teubner-Texte Math., Teubner, Leipzig, 1978. (1978) | MR 0581907 | Zbl 0408.46024

H. Triebel Theory of Function Spaces, Akademische Verlagsgesellschaft Geest & Portig, Lepzig, 1983, und Birkhäuser, Boston, 1983. (1983) | MR 0781540 | Zbl 0546.46028

H. Triebel On Besov-Hardy-Sobolev Spaces in domains and regular elliptic boundary value problems. The case $0

, Comm. Partial Differential Equations 3 (1978), 1083-1164. (1978) | Article | MR 0512083 | Zbl 0403.35034

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. (1984) | Article | MR 0755303

S. A. Williams A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586. (1970) | Article | MR 0267267 | Zbl 0209.13003

E. Zeidler Vorlesungen über nichtlineare Functionalanalysis II - Monotone Operatoren, - Teubner-Texte Math., Teubner, Leipzig, 1977. (1977) | MR 0473928