山路

Because the way will be difficult- I will drive along a mountain road.

因为这个旅途将很漫长。我将一直在山路上行车。

It s difficult to discuss the existence of nontrivial solution for an elliptic equation involving critical exponent.

利用集中紧引理和Hardy不等式克服这个困难，运用山路引理证明了一类非线性椭圆方程非平凡解的存在性

After that the existence of a nontrival solution for the elliptic system is proved by means of Mountain-Pass Lemma. At last, we present two examples to illustrate that our condition is weaker than Boccardo and De.

Figueiredo(2002)的条件更弱的条件下满足条件，并利用山路引理证明了这类拟线性椭圆型方程组非平凡解的存在性，最后举出两个例子验证了文中所给条件的确比Boccardo和De。

The driver sent by the office is an ex-serviceman, and he speaks with admirable accuracy:"5.5 km mountain road to Lower Banyon, 19.5 km highway to GreatLakeTown, and that's a big town."

人武部派的司机也是退伍兵，说话极求精确："下榕树十一华里山路，大湖乡三十九华里公路，那是大镇。"

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths

在科学上没有平坦的大道，只有不畏劳苦沿着陡峭山路攀登的人，才有希望达到光辉的顶点。

Some stages of the race are flat, while others take riders up the steep mountain roads of France. These stages often determine the champion.

比赛中有些赛段很平坦，而有些赛段则车手要骑上法国境内陡峭的山路，而这些赛段也往往决定了冠军人选。

In the condition weaker than the condition, the corresponding functional of the equation is first proved satisfying the condition.

在比条件更弱的条件下，先证明方程相应的泛函满足条件，再应用山路引理得到了该问题无穷多解的存在性。

The road from the summit of Peak Gama to Sun cruise starts as the downhill road.

Pirae 753.9m，北侧是1996年震惊世界的北韩间谍曾经逃跑的山路。

He was seen by a shepherd, gamely negotiating a particularly tricky section of the mountain road to San Doloroso.

牧羊人看见他勇敢地越过了通往圣多鲁鲁的一段崎岖难走的山路。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。