Research
The existence and multiplicity of positive solutions of nonlinear sixth-order boundary value problem with three variable coefficients
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Correspondence: Wanjun Li lwj1965@163.com
Boundary Value Problems 2012, 2012:22 doi:10.1186/1687-2770-2012-22
Published: 22 February 2012Abstract (provisional)
In this article, we discuss the existence and multiplicity of positive solutions for the sixth-order boundary value problem with three variable parameters as follows: \\ $$ \left\{ \begin{array}{lll} u^{(6)}+A(t)u^{(4)}+B(t)u^{(2)}+C(t)u+f(x,u)=0,\\ u(0)=u(1)=u^{''}(0)=u^{''}(1)=u^{(4)}(0)=u^{(4)}(1)\\ \end{array} \right. $$\\ where $A(t),B(t),C(t)\in C[0,1]$, $f(t,u):[0,1]\times[0,\infty)\rightarrow [0.\infty)$ is continuous. The proof of our main result is based upon spectral theory of operators and fixed point theorem in cone.
