They got a sequence of high energy weak solutions whenever (lambda>0) is sufficiently large.
Next we give the standard definition of finite energy weak solutions to the problem (1 - 3) as in [1, 2].
In this paper, we consider a sequence of high energy weak solutions for the modified quasilinear fourth-order elliptic equation (1.1) under rather weak conditions.
The theorem above presents that the energy E of finite energy weak solutions defined on (I=mathbb{R}) is uniformly bounded on (mathbb{R}), and thus we can further construct a set of short trajectories to which any finite energy weak solution is asymptotically attracted by Theorem 1.2.
Under the weaker assumption (lim_{ vert t vert rightarrowinfty}frac{int^{t}_{0}f x,ds,ds}{ vert t vert ^{3}}=infty) uniformly in (xinmathbb{R}^{3}), a sequence of high energy weak solutions for the above problem are obtained.
Let ((rho, mathbf{u})) be a finite energy weak solutions to the problem (1 - 3) and S_{varepsilon}[v]=vartheta_{varepsilon}ast v, quadtextit{where } vartheta _{varepsilon}=vartheta_{varepsilon}(x textit{ is a regularizing sequence}.
For adhesive energies per segment much lower than the thermal energy (weak physisorption) the structure inside the interface and the mobility of octane molecules were found to be liquid-like and quantitatively not very different from the bulk.
Based on Theorem 1.1, we can further get global bounded trajectories of weak solutions to the problem (1 - 3) as in [12], since the family of trajectories generated by the finite energy weak solutions of (1 - 3) defined on I possesses a bounded absorbing set in the energy 'norm'norm
As a significant branch of detection-based techniques, the research of anomaly detection in wired networks and wireless ad hoc networks is already quite mature, but such solutions can be rarely applied to WSNs without any change, because WSNs are characterized by constrained resources, such as limited energy, weak computation capability, poor memory, short communication range, etc.
Jeb Bush was "low energy," "weak," soft" and "sad".
Compared to other spectroscopic methods used in this study, H LF-NMR was found to be highly susceptible to low energy, weak intermolecular interactions, and aggregation of molecules.
