| 1. | Nontrivial solution for a semilinear elliptic equation
一类超线性椭圆方程的非平凡解 |
| 2. | Nontrivial solution for an elliptic equation with singularity
带奇点的二阶椭圆型方程的非平凡解 |
| 3. | The nontrivial solutions for a class of quasilinear elliptic equations
一类非线性椭圆型方程的非平凡广义解 |
| 4. | The approximate analytical expressions of the nontrivial solutions are given to compare with the numerical solutions of the nonlinear problem
最后我们对具体例子进行了数值计算，近似解和数值解的相符表明了分歧分析的有效性。 |
| 5. | The approximate analytical expressions of the nontrivial solutions are given to compare with the numerical solutions of the nonlinear problem
最后我们将理论分析结果与数值方法计算所得结果进行比较，发现是它们是一致的，从而验证了我们的结论。 |
| 6. | A linear impulsive delay difference equation is considered , and snfficient conditions are obtained for the oscillation of nontrivial solutions and asymptotic behaviors of non - oscillatory solutions
摘要研究了一类线性脉冲时滞差分方程，并给出方程非振动解的渐近性态和所有非平凡解振动的判据。 |
| 7. | We introduce liapunov - schmidt reduction method to investigate the bifurcation of a class of nonlinear reaction - diffusion equations in developmental biology . near the bifurcation point we obtain nontrivial solutions branch emitted from the trivial solution
首先，我们引入liapunov - schmidt约化方法，应用到该方程得到该非线性微分方程在分歧点附近分歧方程的解析近似表达式及其非平凡解的渐进表达式。 |
| 8. | In the second part , we consider a class of reaction - diffusion equations in developmental biology . near the bifurcation points , using the liapunove - schmidt reduction process , we obtain the nontrivial solution branches which are bifurcated from the trival solution when the parameter changes
然后考虑发育生物学中一类反应扩散方程组，在分歧点附近利用liapunov - schmidt约化技巧，得到了从平凡解分歧出来的随参数变化的非平凡解枝以及它们的近似解析表达。 |
