Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0704.45013
Pereira, Ducival Carvalho
Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation. (English)
[J] Nonlinear Anal., Theory Methods Appl. 14, No.8, 613-623 (1990). ISSN 0362-546X

Of concern is the existence, uniqueness and asymptotic behavior of solutions to an initial value problem for the second-order equation $$ Ku''(t)+A\sp 2u(t)+M(\vert A\sp{1/2}u(t)\vert\sp 2)\quad Au(t)+u'(t)=0,\quad t\ge 0, $$ in a Hilbert space H. Here $\vert \cdot \vert$ denotes the norm in H, K: $H\to H$ is linear monotone, A is a given linear unbounded operator of H, and M is a real function on $[0,\infty)$. The author extends earlier results by {\it P. Biler} [ibid. 10, 839-842 (1986; Zbl 0611.35057)], and {\it E. H. Brito} [ibid. 8, 1489-1496 (1984; Zbl 0524.35026); ibid. 11, 125-137 (1987; Zbl 0613.34013)].
[S.Aizicovici]

MSC 2000:: *45N05 Integral equations in abstract spaces
45K05 Integro-partial differential equations
34G20 Nonlinear ODE in abstract spaces
35L70 Second order nonlinear hyperbolic equations

Keywords: nonlinear beam equation; existence; uniqueness; asymptotic behavior; initial value problem; second-order equation; Hilbert space; linear unbounded operator

Citations: Zbl 0611.35057; Zbl 0524.35026; Zbl 0613.34013

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.

Advanced Search

Zentralblatt MATH Berlin [Germany]