Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1193.39002
Xu, Youji; Gao, Chenghua; Ma, Ruyun
Solvability of a nonlinear fourth-order discrete problem at resonance. (English)
[J] Appl. Math. Comput. 216, No. 2, 662-670 (2010). ISSN 0096-3003

The authors consider the nonlinear discrete boundary value problem: $$\Delta^4 u(t- 2)= \lambda_1 u(t0= f(t,u(t))+ \tau\varphi(t)+\overline h(t),\quad t\in\Pi_2,$$ $$u(1)= u(T+ 1)= \Delta^2 u(0)= \Delta^2 u(T)= 0,$$ where $T$ is an integer with $T\ge 5$; $\Pi_2= \{2,3,\dots, T\}$; $\lambda_1$ is the first eigenvalue of the associated linear eigenvalue problem; $\varphi(0)$ is the corresponding eigenfunction; $f:\Pi_2\times\bbfR\to\bbfR$ is continuous and $|f(t,s)\le A|s|^\alpha_B$, $t\in\Pi_2$, $s\in\bbfR$ for some $0\le\alpha< 1$ and $A,B\in[0,+\infty)$; $\overline h: \Pi_2\to \bbfR$ with $\sum^T_{s= 2}\overline h(t)\varphi(t)= 0$. The existence of the solution of the above problem is shown.
[Stefan Balint (Timişoara)]

MSC 2000:: *39A12 Discrete version of topics in analysis

Keywords: Krein-Rutman theorem; connectivity of solution set; continuum; fourth-order difference equations; eigenvalue

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]