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Existence of three solutions for a quasilinear two-point boundary value problem. (English) Zbl 1039.34011
The authors investigate a quasilinear second-order differential equation with Dirichlet boundary conditions, i.e., $(\varphi_p(u'))'+\lambda f(t,u)=0$, $u(a)=u(b)=0$, where $\varphi_p(v):=\vert v\vert ^{p-2}v$, $p>1$ is a constant. The existence of an open interval of parameters which ensures this problem admits at least three solutions is determined by using the critical point theory.

34B15Nonlinear boundary value problems for ODE
34B24Sturm-Liouville theory
Full Text: DOI
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