• 제목/요약/키워드: p-Laplacian equation

검색결과 40건 처리시간 0.026초

PERIODIC SOLUTIONS FOR DUFFING TYPE p-LAPLACIAN EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

  • Jiang, Ani
    • Journal of applied mathematics & informatics
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    • 제31권1_2호
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    • pp.27-34
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    • 2013
  • In this paper, we consider the Duffing type p-Laplacian equation with multiple deviating arguments of the form $$({\varphi}_p(x^{\prime}(t)))^{\prime}+Cx^{\prime}(t)+go(t,x(t))+\sum_{k=1}^ngk(t,x(t-{\tau}_k(t)))=e(t)$$. By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation. Moreover, an example is given to illustrate the effectiveness of our results.

ANTI-PERIODIC SOLUTIONS FOR HIGHER-ORDER LIÉENARD TYPE DIFFERENTIAL EQUATION WITH p-LAPLACIAN OPERATOR

  • Chen, Taiyong;Liu, Wenbin
    • 대한수학회보
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    • 제49권3호
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    • pp.455-463
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    • 2012
  • In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

STABILITY FOR A VISCOELASTIC PLATE EQUATION WITH p-LAPLACIAN

  • Park, Sun Hye
    • 대한수학회보
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    • 제52권3호
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    • pp.907-914
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    • 2015
  • In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

REMARKS ON THE INFINITY WAVE EQUATION

  • Huh, Hyungjin
    • 대한수학회보
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    • 제58권2호
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    • pp.451-459
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    • 2021
  • We propose the infinity wave equation which can be derived from the exponential wave equation through the limit p → ∞. The solution of infinity Laplacian equation can be considered as a static solution of the infinity wave equation. We present basic observations and find some special solutions.

POSITIVE SOLUTIONS TO A FOUR-POINT BOUNDARY VALUE PROBLEM OF HIGHER-ORDER DIFFERENTIAL EQUATION WITH A P-LAPLACIAN

  • Pang, Huihui;Lian, Hairong;Ge, Weigao
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.59-74
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    • 2010
  • In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

THE NEHARI MANIFOLD APPROACH FOR DIRICHLET PROBLEM INVOLVING THE p(x)-LAPLACIAN EQUATION

  • Mashiyev, Rabil A.;Ogras, Sezai;Yucedag, Zehra;Avci, Mustafa
    • 대한수학회지
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    • 제47권4호
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    • pp.845-860
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    • 2010
  • In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.