Existence of Non-negative Solutions of Nonlinear Third order Eigenvalue Problems
The authors consider the nonlinear third order differential equationsu+ρ~3u=λg(t)f(u),\ 0t2π(B)with the periodic boundary conditionsu~((i))(0)=u~((i))(2π),\ i=0,1,2(E)Where ρ∈0,13 is a constant,λ0 is a parameter.Two results on the existence of non-negative solutions to problem(B)-(E) are obtained.And the proof uses the fixed point ndex in the cone theory.
In this paper, we study the qualitative behavior of following open-access anchovy fishery model:    c x p y y y x d ax x v n n n n v n b n n    , where   , , , , , , , p v d c b a and the initial conditions 0 0 , y x are positive real numbers. More precisely, we investigate the necessary and sufficient condition for local asymptotic stability of the unique positive equilibrium point of this system. Some numerical examples are given to verify our theoretical results.