On the solvability of nonlinear elliptic equations in Sobolev spaces

• Autorzy: Piotr Fijałkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J65: Nonlinear boundary value problems for linear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 2
• Strony: 149-156

Daty

wydano

1992

otrzymano

1990-08-01

poprawiono

1991-01-15

Twórcy

autor

Piotr Fijałkowski

• Institute of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland

Bibliografia

• [1] S. N. Bernstein, Sur les équations du calcul des variations, Ann. Sci. École Norm. Sup. 29 (1912), 431-485.
• [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.
• [4] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985).
• [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin 1983.
• [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.