TY - JOUR AU - Heidarkhani, Shapour AU - Henderson, Johnny PY - 2016/04/12 Y2 - 2024/03/29 TI - Critical point approaches to quasilinear second order differential equations depending on a parameter JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 44 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2014.042 SP - 177 - 197 AB - In this paper, we make application of some three-critical pointsresults to establish the existence of at least three solutionsfor a boundary value problem for the quasilinear second order differential equation on a compact interval $[a,b]\subset\mathbb{R}$,$$\cases-u''=(\lambda f(x,u)+g(x,u))h(x,u') &\text{\rm in } (a,b),\\u(a)=u(b)=0,\endcases$$ under appropriate hypotheses. We exhibit theexistence of at least three (weak) solutions. ER -