# On the solvability of nonlinear elliptic equations in Sobolev spaces

Annales Polonici Mathematici (1992)

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

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topPiotr 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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- [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] 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] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985). Zbl0615.34010
- [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin 1983. Zbl0521.35002
- [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] N. G. Lloyd, Degree Theory, Cambridge Univ. Press, 1978.
- [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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