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Zbl 1221.34062
Feng, Meiqiang
Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions.
(English)
[J] Appl. Math. Lett. 24, No. 8, 1419-1427 (2011). ISSN 0893-9659

The author studies the existence of symmetric positive solutions for the nonlinear nonlocal boundary problem $$(g(t)x'(t))'+w(t)f(t,x(t))=0,$$ $$ax(0)-b\lim_{t\to 0^+} g(t)x'(t)=\int^1_0h(s)x(s)\,ds,\quad ax(1)+b\lim_{t\to 1^{-}} g(t)x'(t)=\int^1_0h(s)x(s)\,ds,$$ where $a,b>0$, $g\in C^1([0,1], (0, \infty))$, $w\in L^p(0,1)$ and $h\in L^1((0,1),(0,\infty))$ are symmetric on $[0,1]$, respectively; $f:[0,1]\times [0,\infty)\to [0,\infty)$ is continuous and $f(t, x)=f(1-t,x)$. The main tool is the theory of fixed point index.
[Ruyun Ma (Lanzhou)]
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B10 Multipoint boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: integral boundary conditions; fixed point index theorem; existence of solutions;

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