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Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions. (English) Zbl 1221.34062

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)-blim t0 + g(t)x ' (t)= 0 1 h(s)x(s)ds,ax(1)+blim t1 - g(t)x ' (t)= 0 1 h(s)x(s)ds,

where a,b>0, gC 1 ([0,1],(0,)), wL p (0,1) and hL 1 ((0,1),(0,)) are symmetric on [0,1], respectively; f:[0,1]×[0,)[0,) is continuous and f(t,x)=f(1-t,x). The main tool is the theory of fixed point index.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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