By a weak version of the mountain pass lemma, there is a mountain pass point (u_{3}).
Ang Lee is normally such an expert calibrator of performances — there wasn't a weak link in "Brokeback Mountain" — that it's a shock to find both overwhelmers and underwhelmers at loose in his latest work.
After a weak day in the mountains and a fourth-place finish by van Garderen in last Monday's time trial, Taaramae had to give the jersey back.
A new result is obtained under more relaxed conditions by using the mountain pass theorem, a weak convergence argument, and a weak version of Lieb's lemma.
A sufficient condition is obtained for the existence of nontrivial weak homoclinic orbits of second-order impulsive differential equations by employing the mountain pass theorem, a weak convergence argument and a weak version of Lieb's lemma.
By using the mountain pass theorem, a weak convergence argument, and a weak version of Lieb's methods, Fang and Duan [1] investigated homoclinic solutions of problem (1.2) and obtained the following main result.
Motivated by the works of Nieto and Regan [7], Smets and Willem [13], in this paper we study the existence of nontrivial weak homoclinic orbits of (1.1 - 1.2 1.1 - 1.2 the mountain pass theorem, a weak version of Liebys lemma and a weak convergence argusing.
Early snow in the fall coupled with rain left a weak, ice-covered base on many mountains.
"Rather, another mountain to climb," he said with a weak smile.
In this way we obtain a weak solution in (W_{0,G}^{1,p}(S)) for our problem using the mountain pass theorem of Ambrosetti and Rabinowitz [22].
