Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MULTIPLICITY RESULTS OF POSITIVE SOLUTIONS FOR SINGULAR GENERALIZED LAPLACIAN SYSTEMS

  • Lee, Yong-Hoon (Department of Mathematics Pusan National University) ;
  • Xu, Xianghui (School of Mathematics and Statistics Science Ludong University)
  • Received : 2018.09.28
  • Accepted : 2018.12.10
  • Published : 2019.09.01
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Abstract

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

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References

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