The differential inequality theory and diagonalization method , as two effective tools in solving singular perturbation problems , have developed rapidly in the recent several decades
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The initial boundary value problems for the reaction diffusion equations are considered . and the asymptotic behavior of solution for the problem is obtained by using the theory of differential inequality
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Under appropriate assumptions , the existence of solution is proved by means of the theory of differential inequalities and the uniformly valid asymptotic expansion for arbitrary nthorder is obtained
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Under suitable conditions , using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied , which reduced problems possess two intersecting solutions
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By introducing proper stretchy variable and constructing boundary layer function , it concludes n - order approximate solution , and using theory of differential inequality , uniformly validity of asymptotic expansion is proved
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On the basis of the formal asymptotic solutions having been constructed for the singularly perturbed problems , the formal asymptotic solutions for the original problems are proved by using the differential inequalities and the fixed point theorems
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This paper discusses the positive periodic solution and the almost periodic solution to dimensional predator - prey model with prey supplements by using the differential inequality , and its stability under disturbances in the shell
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By using differential inequality , comparable theory and the lyapunov functional we obtain some sufficient conditions that guarantee the permanence of the species and some sufficient conditions that guarantee every positive solution global attractivity . and if the system is a
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The paper studies the existence and global exponential convergence of alomost periodic solutions for high - order neural networks involving variable delay by applying the theory of fixed point and differential inequality technique , some new criteria on the existence and global exponential convergence of almost periodic solutions are obtained
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