Stationary solutions for a 1D pde problem with gradient term and negative powers nonlinearity

Traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity

“…This improvement is described in detail in Subsection 4.1. Furthermore, this improvement has already been introduced into [12], and the asymptotic behavior, which was previously difficult to derive, has been obtained. However, the underlying idea is similar to the previous ones.…”

“…Note that the basic idea is the same as the previous ones. However, the detailed principal part is chosen as carefully as in [12] (see Remark 2.4).…”

“…Furthermore, (1.1) and (1.2) are special cases of the generalized MEMS type partial differential equation (see [5,8,12] and references therein). The MEMS model is the Micro-Electro Mechanical System devices and used in many machines around us (for instance, see [16]).…”

Radially symmetric stationary solutions for a MEMS type reaction–diffusion equation with fringing field

“…Here we note that for the one-dimensional case (2), the results stated in [12] cannot be obtained by applying the computations shown in the later sections of this paper straightforwardly (see [12] for the details). Moreover, for N = 2, the dynamics associated with the radially symmetric stationary problem of ( 1) is not topologically equivalent to the case with N 3.…”

“…Here, α ∈ 2N, 2 = β ∈ 2N, μ > 0, and δ 0. In [12], the existence, profiles, and asymptotic behaviour of the stationary solutions of (2) are studied by applying Poincaré-Lyapunov compactification and dynamical systems theory. Additionally, we note that the results follow from the analysis of the dynamics at infinity.…”