Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0853.34021
Mawhin, Jean
Some remarks on semilinear problems at resonance where the nonlinearity depends only on the derivatives. (English)
[J] Acta Math. Inform. Univ. Ostrav. 2, No.1, 61-69 (1994). ISSN 1211-4774

The author considers the Neumann and the periodic boundary value problems for the second order nonlinear system $u'' + g(t,u') = f(t)$, $t \in [a,b]$, where $f \in L^1 ([a,b], \bbfR^n)$ and $g : [a,b] \times \bbfR^n \to \bbfR^n$ is a Carathéodory function such that (1) $g(t,v)/ |v |\to 0$ uniformly a.e. in $t \in [a,b]$ whenever $|v |\to \infty$. In particular, he shows that for each $\widetilde f \in L^1 ([a,b], \bbfR^n)$ such that $(\int^b_a \widetilde fds)/(b - a) = 0$ there exist $k \in \bbfR^n$ such that the given problem with $f = \widetilde f + k$ possesses a family of solutions of the form $u(t) + c$, $c \in \bbfR^n$. In the scalar case $n = 1$ analogous existence results are obtained if $g$ is continuous ((1) need not be satisfied) and $f \in L^2 ([a,b], \bbfR)$. Some uniqueness results are given, as well.
[M.Tvrdý (Praha)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34C25 Periodic solutions of ODE

Keywords: periodic boundary value problems; second order nonlinear system; uniqueness

Cited in: Zbl 1033.34021

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]