On the solvability of nonlinear elliptic equations in Sobolev spaces

Piotr Fijałkowski

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 149-156
  • ISSN: 0066-2216

Abstract

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We consider the existence of solutions of the system (*) P ( D ) u l = F ( x , ( ∂ α u ) ) , l = 1,...,k, x ∈ ℝ n ( u = ( u ¹ , . . . , u k ) ) in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.

How to cite

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Piotr Fijałkowski. "On the solvability of nonlinear elliptic equations in Sobolev spaces." Annales Polonici Mathematici 56.2 (1992): 149-156. <http://eudml.org/doc/262349>.

@article{PiotrFijałkowski1992,
abstract = {We consider the existence of solutions of the system (*) $P(D)u^l = F(x,(∂^α u))$, l = 1,...,k, $x ∈ ℝ^n$$(u=(u¹,...,u^k))$ in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.},
author = {Piotr Fijałkowski},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear elliptic equations; existence; Sobolev spaces},
language = {eng},
number = {2},
pages = {149-156},
title = {On the solvability of nonlinear elliptic equations in Sobolev spaces},
url = {http://eudml.org/doc/262349},
volume = {56},
year = {1992},
}

TY - JOUR
AU - Piotr Fijałkowski
TI - On the solvability of nonlinear elliptic equations in Sobolev spaces
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 149
EP - 156
AB - We consider the existence of solutions of the system (*) $P(D)u^l = F(x,(∂^α u))$, l = 1,...,k, $x ∈ ℝ^n$$(u=(u¹,...,u^k))$ in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.
LA - eng
KW - nonlinear elliptic equations; existence; Sobolev spaces
UR - http://eudml.org/doc/262349
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, E. H. Zarantonello (ed.), Academic 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] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985). Zbl0615.34010
  5. [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin 1983. Zbl0521.35002
  6. [6] M. A. Krasnosel'skiĭ, P. P. Zabreĭko, E. I. Pustyl'nik and P. E. Sobolevskiĭ, Integral Operators in Spaces of Summable Functions, Nauka, Moscow 1966 (in Russian). 
  7. [7] N. G. Lloyd, Degree Theory, Cambridge Univ. Press, 1978. 
  8. [8] B. Przeradzki, On the solvability of singular BVPs for second-order ordinary differential equations, Ann. Polon. Math. 50 (1990), 279-289. Zbl0701.34006

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