On a class of nonlinear ellipticequations in Hilbert spaces

• Autorzy: Piotr Fijałkowski
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

nonlinear elliptic boundary value problems  

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 3
• Strony: 203-213

Daty

wydano

1994

otrzymano

1992-10-28

poprawiono

1993-03-03

poprawiono

1993-07-05

Twórcy

autor

Piotr Fijałkowski

• Institute of Mathematics, University of Łódź, S. 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, Acad. 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] P. Fijałkowski, On the solvability of nonlinear elliptic systems in Sobolev spaces, ibid. 56 (1992), 149-156.
• [5] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985).
• [6] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin, 1983.
• [7] K. J. Palmer, On the complete continuity of differentiable mappings, J. Austral. Math. Soc. 9 (1969), 3-4.
• [8] B. Przeradzki, On the solvability of singular BVP's for second-order ordinary differential equations, Ann. Polon. Math. 50 (1990), 279-289.
• [9] K. Yosida, Functional Analysis, Springer, Berlin, 1980.