• Title, Summary, Keyword: p-Laplacian

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Upper and lower solutions for a singular p-Laplacian system

  • Kim, Chan-Gyun;Lee, Eun-Kyoung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.89-99
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    • 2007
  • In this paper, we define the upper and lower solutions for a p-Laplacian system with singular nonlinearity at the boundaries. And we prove the theorem for the upper and power solutions method.

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THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

  • Chung, Soon-Yeong;Lee, Hee-Soo
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.591-601
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    • 2011
  • In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

MULTIPLE SOLUTIONS FOR A p-LAPLACIAN SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

  • Zhou, Jun;Kim, Chan-Gyun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.99-113
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    • 2014
  • A nonlinear elliptic problem involving p-Laplacian and nonlinear boundary condition is considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameter is small enough.

THREE SOLUTIONS TO A CLASS OF NEUMANN DOUBLY EIGENVALUE ELLIPTIC SYSTEMS DRIVEN BY A (p1,...,pn)-LAPLACIAN

  • Afrouzi, Ghasem A.;Heidarkhani, Shapour;O'Regan, Donal
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1235-1250
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    • 2010
  • In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.