具有p-Laplacian拟线性特征值Dirichlet问题的多重解

Multiplicity of Solutions for Quasilinear Eigenvalue Dirichlet Problems with p-Laplacian

利用变分方法和Ricceri三临界点定理,建立了一类具有p-Laplacian的非线性特征值问题:-(u′(t)p-2u′(t))′+a(t)up-2u=λf(u(t)),a<t<b,u(a)=u(b)=0,至少存在3个弱解的充分条件,并且推广了已有文献的相关结果.

Using variational method and a three critical points theorem of Ricceri, we considered a class of quasilinear eigenvalue problem of the form {-（｜u′（t）｜^p-2u′（t））′＋a（t）｜u｜^p-2u=λf（u（t））,a〈t〈b,u（a）=u（b）=0,and sufficient conditions which guarantee the existence of at least three weak solutions for the above problem were established. Moreover, the results in the literature are generalized.