1) positive entire solution
正整解
1.
The existence and properties of positive entire solutions for a class of singular nonlinear biharmonic equations on R~n;
一类R~n上奇异非线性双调和方程正整解的存在性及性质
2.
Existence and properties of positive entire solutions for a class of polyharmonic equations;
一类多重调和方程的正整解的存在性及其性质
3.
A note on positive entire solution to a singular nonlinear elliptie epuation;
关于奇异非线性椭圆型方程正整解的一点注记
2) positive integral solution
正整数解
1.
With a recursive sequence,quadratic remainder and congruence,the diophantine equation x2-3y4=97 is proved that it has only positive integral solutions(x,y)=(10,1).
运用递归数列,同余式和平方剩余证明了不定方程x2-3y4=97仅有正整数解(x,y)=(10,1)。
2.
Let p be a prime number,using Fermat Infinite method of descent,to study the positive integral solution of the equations x~4±3px~2y~2+3p~2y~4=z~(2) and x~4±6px~2y~2-3p~2y~4=z~(2).
设p为素数,利用F erm at无穷递降法,研究方程x4±3px2y2+3p2y4=z2与x4±6px2y2-3p2y4=z2正整数解的存在性,证明该方程在p≡5(m od 12)时均无正整数解,在p≡11(m od 12)时有解且有无穷多组正整数解,获得方程无穷多组正整数解的通解公式和方程的部分正整数解。
3.
By using computer language, we get all the positive integral solution of x2±xy+y2 = P and x2±xy+y2 = 3p within the scope of arbitrarily.
讨论了方程x2±xy+y2=k的可解性,利用C语言编写出方程x2±xy+y2=p和x2±xy+y2=3P的计算程序,并获得方程在一定范围内的所有正整数解。
3) positive integer solution
正整数解
1.
An equation involving the pseudo Smarandache function and its positive integer solutions;
关于伪Smarandache函数的一个方程及其正整数解
2.
On the necessary condition of one class of hyperelliptic equations having the positive integer solutions;
一类超椭圆方程有正整数解的必要条件的问题
3.
A function equation related to the Smarandache function and its positive integer solutions;
一个与Smarandache函数有关的函数方程及其正整数解
4) positive integer solutions
正整数解
1.
The Positive Integer Solutions of the Indefinite Equationx~2+(k-1)y~2=kz~2 & x~(k+2)-x~k =py~k;
不定方程x~2+(k-1)y~2=kz~2与x~(k+2)-x~k=py~k的正整数解
2.
An equation involving the functions Z(n) and D(n) and its all positive integer solutions
一个包含Z(n)和D(n)函数的方程及其它的正整数解
3.
An equation involving the Euler function and the Smarandache ceil function of k order and its positive integer solutions
一个包含Euler函数及k阶Smarandache ceil函数的方程及其正整数解
5) positive entire solution
正整体解
1.
Existence of positive entire solutions of singular semilinear elliptic systems;
关于奇异半线性椭圆型方程组的正整体解的存在性
2.
Sufficient and necessary conditions for the existence of positive entire solutions of a class of quasilinear elliptic systems;
一类拟线性椭圆型方程组的正整体解存在的充分必要条件
3.
This paper investigates the existence of positive entire solutions to a class of nonlinear second order elliptic equations with singularity in Rn (n≥3).
本文研究了Ｒｎ（ｎ≥３）中一类带奇异性的非线性二阶椭圆方程正整体解的存在性。
6) positive entire solutions
正整体解
1.
On the positive entire solutions to a class of semilinear elliptic equations;
一类半线性椭圆方程的正整体解及其渐近性态
2.
The existence of positive entire solutions of a class of singular, p-Laplace equations;
奇异p-Laplace方程的正整体解的存在性
3.
The existence of positive entire solutions for a class of semilinear elliptic equations in Rn is discussed.
首先给出此方程的径向解 ,并以它及上下解为主要工具证明了在不同条件下方程存在正整体解 。
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