On the solvability of nonlinear elliptic equations in Sobolev spaces
Piotr Fijałkowski
Annales Polonici Mathematici, Tome 57 (1992), p. 149-156 / Harvested from The Polish Digital Mathematics Library
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We consider the existence of solutions of the system (*) P(D)ul=F(x,(∂αu)), l = 1,...,k, x∈ℝn (u=(u¹,...,uk)) in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:262349 
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     year = {1992},
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Piotr Fijałkowski. On the solvability of nonlinear elliptic equations in Sobolev spaces. Annales Polonici Mathematici, Tome 57 (1992) pp. 149-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z2p149bwm/

[00000] [1] S. N. Bernstein, Sur les équations du calcul des variations, Ann. Sci. École Norm. Sup. 29 (1912), 431-485. | Zbl 43.0460.01

[00001] [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.

[00002] [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. | Zbl 0739.34004

[00003] [4] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985). | Zbl 0615.34010

[00004] [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin 1983. | Zbl 0521.35002

[00005] [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).

[00006] [7] N. G. Lloyd, Degree Theory, Cambridge Univ. Press, 1978.

[00007] [8] B. Przeradzki, On the solvability of singular BVPs for second-order ordinary differential equations, Ann. Polon. Math. 50 (1990), 279-289. | Zbl 0701.34006