On a class of nonlinear ellipticequations in Hilbert spaces

Piotr Fijałkowski

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 203-213
  • ISSN: 0066-2216

Abstract

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We consider elliptic nonlinear equations in a separable Hilbert space and their solutions in spaces of Sobolev type.

How to cite

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Piotr Fijałkowski. "On a class of nonlinear ellipticequations in Hilbert spaces." Annales Polonici Mathematici 59.3 (1994): 203-213. <http://eudml.org/doc/262274>.

@article{PiotrFijałkowski1994,
abstract = {We consider elliptic nonlinear equations in a separable Hilbert space and their solutions in spaces of Sobolev type.},
author = {Piotr Fijałkowski},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear elliptic boundary value problems; finite dimensional approximation},
language = {eng},
number = {3},
pages = {203-213},
title = {On a class of nonlinear ellipticequations in Hilbert spaces},
url = {http://eudml.org/doc/262274},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Piotr Fijałkowski
TI - On a class of nonlinear ellipticequations in Hilbert spaces
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 203
EP - 213
AB - We consider elliptic nonlinear equations in a separable Hilbert space and their solutions in spaces of Sobolev type.
LA - eng
KW - nonlinear elliptic boundary value problems; finite dimensional approximation
UR - http://eudml.org/doc/262274
ER -

References

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  1. [1] S. N. Bernstein, Sur les équations du calcul des variations, Ann. Sci. École Norm. Sup. 29 (1912), 431-485. Zbl43.0460.01
  2. [2] F. E. Browder, Nonlinear functional analysis and nonlinear integral equations of Hammerstein and Urysohn type, in: Contributions to Nonlinear Functional Analysis, Acad. Press, New York, 1971, 425-500. 
  3. [3] P. Fijałkowski, On the equation x''(t) = F(t,x(t)) in the Sobolev space H¹(ℝ), Ann. Polon. Math. 53 (1991), 29-34. Zbl0739.34004
  4. [4] P. Fijałkowski, On the solvability of nonlinear elliptic systems in Sobolev spaces, ibid. 56 (1992), 149-156. Zbl0776.35017
  5. [5] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985). Zbl0615.34010
  6. [6] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin, 1983. Zbl0521.35002
  7. [7] K. J. Palmer, On the complete continuity of differentiable mappings, J. Austral. Math. Soc. 9 (1969), 3-4. Zbl0174.19303
  8. [8] B. Przeradzki, On the solvability of singular BVP's for second-order ordinary differential equations, Ann. Polon. Math. 50 (1990), 279-289. Zbl0701.34006
  9. [9] K. Yosida, Functional Analysis, Springer, Berlin, 1980. 

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