Applied Mathematics and Mechanics (English Edition) ›› 1988, Vol. 9 ›› Issue (5): 423-433.

• Articles •     Next Articles

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR A VECTOR FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATION

Lin Zong-chi1, Lin Su-rong2   

  1. 1. Fujian Normal University, Fuzhou;
    2. Fujian Broadcasting TV University, Fuzhoii
  • Received:1987-02-20 Online:1988-05-18 Published:1988-05-18

Abstract: We study the vector boundary value problem with boundary perturbations: ε2y(4)=f(x,u,y",ε,μ) (μx-μ=A1(ε,μ),y(x,ε,μ)|x-μ=B1(ε,μ) y"(x,ε,μ)|x-μ=A2(ε,μ),y"(x,ε,μ)|x-μ=B2(ε,μ) where yf, Aj and Bj (j=1,2) are n-dimensional vector functions and ε, μ are two small positive parameters. This vector boundary value problem does not appear to have been studied, although the scalar boundary value problem has been treated. Under appropriate assumptions, using the method of differential inequalities we find a solution of the vector boundary value problem and obtain the uniformly valid asymptotic expansions.

Key words: renewable resource, optimal harvesting, stability, bifurcation, limit cycle

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