Multiple solutions of Sturm–Liouville boundary value problem via lower and upper solutions and variational methods Original Research Article

In this paper, we prove the existence of multiple solutions for second order Sturm–Liouville boundary value problem View the MathML source{−Lu=f(x,u),x∈[0,1]R1(u)=0,R2(u)=0, Turn MathJax on where Lu=(p(x)u′)′−q(x)uLu=(p(x)u′)′−q(x)u is a Sturm–Liouville operator, R1(u)=αu′(0)−βu(0)R1(u)=αu′(0)−βu(0), R2(u)=γu′(1)+σu(1)R2(u)=γu′(1)+σu(1). The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the existence of four solutions and seven solutions is given.