New existence results on nonhomogeneous Sturm–Liouville type BVPs for higher-order $p$-Laplacian differential equations

Tom 38 / 2011

Yuji Liu Applicationes Mathematicae 38 (2011), 295-314 MSC: Primary 34B10; Secondary 34B15. DOI: 10.4064/am38-3-3


A class of nonlinear boundary value problems for $p$-Laplacian differential equations is studied. Sufficient conditions for the existence of solutions are established. The nonlinearities are allowed to be superlinear. We do not apply the Green's functions of the relevant problem and the methods of obtaining a priori bounds for solutions are different from known ones. Examples that cannot be covered by known results are given to illustrate our theorems.


  • Yuji LiuDepartment of Mathematics
    Guangdong University of Business Studies
    Guangzhou 510000, P.R. China

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