Three positive solutions of a nonlinear three-point boundary value problem

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem <fen><cp type="lcub" STYLE="S"><ar><r><c CSPAN="1" RSPAN="1" CA="L" RA="T">u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1),</c></r><r><c CSPAN="1" RSPAN="1" CA="L" RA="T">u(0)=0, u(1)=αu(η),</c></r></ar></fen> are established by using the Leggett–Williams fixed point theorem. An example is also included to illustrate the importance of the result obtained. [Copyright &y& Elsevier]