Positive solutions for one-dimensional singular $p$-Laplacian boundary value problems

Tom 105 / 2012

Huijuan Song, Jingxue Yin, Rui Huang Annales Polonici Mathematici 105 (2012), 125-144 MSC: Primary 35J70; Secondary 35J25. DOI: 10.4064/ap105-2-2

Streszczenie

We consider the existence of positive solutions of the equation $$ {1\over \lambda (t)}(\lambda (t)\varphi _p(x'(t)))'+ \mu f(t,x(t),x'(t))=0, $$ where $\varphi _p(s)=|s|^{p-2}s, p>1$, subject to some singular Sturm–Liouville boundary conditions. Using the Krasnosel'skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.

Autorzy

  • Huijuan SongDepartment of Mathematics
    Jilin University
    Changchun 130012, China
    e-mail
  • Jingxue YinSchool of Mathematical Sciences
    South China Normal University
    Guangzhou 510631, Guangdong, China
    e-mail
  • Rui HuangSchool of Mathematical Sciences
    South China Normal University
    Guangzhou 510631, Guangdong, China
    e-mail

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