Critical point approaches to quasilinear second order differential equations depending on a parameter

Shapour Heidarkhani, Johnny Henderson

Abstract


In this paper, we make application of some three-critical points
results to establish the existence of at least three solutions
for 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 the
existence of at least three (weak) solutions.

Keywords


Dirichlet problem; critical point; three solutions; variational methods

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