Amazonian forest cleared in Ecuador, a mountain levelled in Peru, the Cerrado savannah converted to soy fields in Brazil and oil fields under development in Venezuela's Orinoco belt.
The first hour was full of fantastic scenery as we climbed up to 4,725m over La Cumbre pass in the mountains, level with the snow line.
This is a smashed, brutal landscape, its mountains levelled, its rivers blocked.
The building blocks are one-bump solutions at the mountain pass level and the existence of such solutions as well as multi-bump solutions is guaranteed by a nondegeneracy assumption of the solutions near the mountain pass level.
By Theorem 4.2 in [12], the mountain pass level d can be characterized as d = inf u ∈ N J ˜ ( u ).
Also as remarked in [2], [12], the mountain pass level d can be characterized by (1.6) provided (2.1), (2.2), and (2.3) hold.
By Lemma 2.3 and Lemma 2.4, we see that the Palais-Smale sequence ({u_{n}}) at the mountain pass level c is bounded in E and its weak limit u is a critical point of the functional I.
We prove that, when the initial energy is smaller than the mountain pass level corresponding to the stationary equation of (1.1) (see (1.7) and Lemma 4.1), the initial Nehari functional plays an important role in determining asymptotic behavior of the solution of (1.1), see Theorem 1.1.
The authors in [9] first considered problem (1 - 3) and obtained the global existence and blow up of solutions for the sub-critical case (E(0)< d), where (E(0)) is the initial energy and d is the depth of the potential well or the mountain pass level, which will be defined later.
