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2 results

  • PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

  • Part of
  • JIFENG CHU, ZIHENG ZHANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 3 / December 2010
    Published online by Cambridge University Press:
    14 September 2010, pp. 437-445
    Print publication:
    December 2010
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  • In this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

  • TRAVELLING WAVE SOLUTIONS IN NONLOCAL REACTION–DIFFUSION SYSTEMS WITH DELAYS AND APPLICATIONS

  • Part of
  • ZHI-XIAN YU, RONG YUAN
  • Journal:
    The ANZIAM Journal / Volume 51 / Issue 1 / July 2009
    Published online by Cambridge University Press:
    09 March 2010, pp. 49-66
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  • This paper deals with two-species convolution diffusion-competition models of Lotka–Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder’s fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour.