On boundary value problem for a nonlocal elliptic equation

• Autorzy: Fijałkowski P. , Przeradzki B.
• Języki publikacji: EN

Abstrakty

EN

The existence of a positive radial solution to the Dirichlet boundary value problem for the second order elliptic equation [wzór], where U = B(0, R) \ ‾B(0, ρ), with weak assumptions on the nonlinear term f, is proved. The method based on the Krasnosel'skii Fixed Point Theorem enables to find many solutions to the problem. Solutions for the same problem but with U = B(0, R) and with nonlinear term f depending explicitely on |x| are found as well.

Słowa kluczowe

EN

nonlocal equation; cone; fixed point; radial solution

PL

nielokalne równanie; stożek; punkt stały; rozwiązanie radialne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2003
• Tom: Vol. 9, nr 2
• Strony: 201--209
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Fijałkowski P.

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

autor

Przeradzki B.

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

Bibliografia

• [1] Bebernes, J., Lacey, A. A., Global existence and finite-time blow-up for a class of nonlocal parabolic problems, Adv. Differential Equations 2(6) (1997), 927-953.
• [2] Guo, D., Lakshmikantham, V., Nonlinear Problems in Abstract Cones, Acad. Press, Inc., Boston, MA, 1988.
• [3] Krasnosel’skii, M., Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, 1964.
• [4] Krzywicki, A., Nadzieja, T., Nonlocal elliptic problems. Evolution equations: existence, regularity and singularities, Banach Center Publ. 52 (2000), Polish Acad. Sci., Warsaw, 147-152.
• [5] Ni, W., Nussbaum, N., Uniqueness and nonuniqueness for positive radial solutions of ∆u + f(u,r) = 0, Comm. Pure Appl. Math. 38 (1985), 67-108.
• [6] Przeradzki, B., Stańczy, R., Positive solutions for sublinear elliptic equations, Colloq. Math. 92 (2002), 141-151.
• [7] Stańczy, R., Nonlocal elliptic equations, Nonlinear Anal. 47 (2001), 3579-3584.