Related papers: Mountain pass type solutions for a generalized Fre…
We study a generalized Frenkel-Kontorova model. Using minimal and Birkhoff solutions as building blocks, we construct a lot of homoclinic solutions and heteroclinic solutions for this generalized Frenkel-Kontorova model under gap…
We study heteroclinic solutions of a generalized Frenkel-Kontorova model. Using the methods of Rabinowitz and Stredulinsky, we prove that if the rotation vector of the configuration is rational and if there is an adjacent pair of periodic…
We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that is sufficiently small in the space of square integrable…
A discrete Frenkel-Kontorova model with two alternate spring constants $k_{1}$ and $k_{2}$ is studied. It is found that this model has many surprising behaviours. The continuum version of this model is different from the sine-Gordon…
The Ghoussoub-Preiss's generalized Mountain Pass Lemma with Cerami-Palais-Smale type condition is a generalization of classical MPL of Ambrosetti-Rabinowitz, we apply it to study the existence of the periodic solutions with a given energy…
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field…
Using Struwe's "monotonicity trick" and the recent blow-up analysis of Ohtsuka and Suzuki, we prove the existence of mountain pass solutions to a mean field equation arising in two-dimensional turbulence.
We construct new traveling wave solutions of moving kink type for a modified, driven, dynamic Frenkel-Kontorova model, representing dislocation motion under stress. Formal solutions known so far are inadmissible for velocities below a…
Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schr\"{o}dinger equation involving critical exponent in ${\BR}^N$. These equations contain strongly singular nonlinearities…
We study the existence and multiplicity of positive solutions in $H^1(\mathbb{R}^N)$, $N\ge3$, with prescribed $L^2$-norm, for the (stationary) nonlinear Schr\"odinger equation with Sobolev critical power nonlinearity. It is well known…
The Frenkel-Kontorova model is a simple yet generic framework for the description of tribological phenomena and processes, including dry solid friction and the motion of adsorbed layers. As revealed in this work, it also reproduces…
The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular…
A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci.,…
We extend the De Giorgi--Nash--Moser theory to a class of kinetic Fokker-Planck equations and deduce new results on the Landau-Coulomb equation. More precisely, we first study the H{\"o}lder regularity and establish a Harnack inequality for…
We present a method to investigate the kinetics of protein folding on a long time-scale and the dynamics underlying the formation of secondary and tertiary structures during the entire reaction. The approach is based on the formal analogy…
We derive two different generalized heat-transport equations: The most general one, of the first order in time and second order in space, encompasses some well known heat equations and describes the hyperbolic regime in the absence of…
We obtain a pair of nontrivial solutions for a class of concave-linear-convex type elliptic problems that are either critical or subcritical. The solutions we find are neither local minimizers nor of mountain pass type in general. They are…
Recently, it has been claimed (O. V. Gendelman and A. V. Savin, Phys. Rev. Lett. {\bf 84}, 2381 (2000); A.V.Savin and O.V.Gendelman, arXiv: cond-mat/0204631 (2002)) that two nonlinear classical 1-d lattice models show transitions, at finite…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known…