Existence of infinitely many homoclinic orbits in discrete Hamiltonian systems

By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n−1)]−L(n)u(n)+∇W(n,u(n))=0 has infinitely many homoclinic orbits, where n∈Z, u∈RN, p,L:Z→RN×N and W:Z×RN→R are no periodic in n. Our conditions on the potential W(n,x) are rather relaxed.     

Boundary value problems of second order nonlinear functional difference equations

By using the critical point theory, some sufficient conditions for the existence and multiplicity of the boundary value problems to a class of second order functional difference equations are obtained.     

Looking back at perpendicular magnetic recording R&D in NEC

This paper reports perpendicular magnetic recording (PMR) circumstances and the results based on the reference published by NEC. The PMR flexible disks using Co-Cr-Ta films were investigated. Pass wear durability of Co-Cr-Ta film strongly depends on the base film surface roughness and Young's modulus values of Co-Cr-Ta films. Pass wear durability, more than 10 million passes, was confirmed under a high temperature (60 °C) and a high humidity (80% RH) condition, as well as a low temperature (5 °C) condition. The read/write characteristics for double-layered PMR media were examined by using a combination of a single-pole-type (SPT) write head and a magnetoresistive (MR) read head, and a conventional merged ring type inductive (ID) write head/MR read head. By differential equalization of the reproduced voltage, the bit error rate less than 10⁻⁶ at 3 Gb/in.² was obtained for the SPT/MR head combination. The antenna effect for PMR realization was analyzed using the merged ring type ID/MR head. In order to increase the magnetic circuit resistance from the ID head pole to the soft underlayer, we developed the sendust (FeAlSi) soft underlayer with low magnetic permeability. We confirmed that the recorded signal has better stability under the ID/MR head-loaded condition than the SPT head-loaded condition. These results show that there are the head and media solutions to realize PMR. We had confidence that we could use the basic structure of the commercial ID/MR head for the PMR head.     

MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM

Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.     

Singular quasilinear elliptic problems with indefinite weights and critical potential

The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN , is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.     

INFINITELY MANY SOLUTIONS TO p（x）-BIHARMONIC PROBLEM WITH NAVIER BOUNDARY CONDITIONS

In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.     

On some nonlinear elliptic problems for p–Laplacian in \mathbb {R}^N

In this paper, we consider a nonlinear elliptic problem involving the p-Laplacian with perturbation terms in the whole . Via variational arguments, we obtain existence and regularity of nontrivial solutions. The research of the first and second authors is supported by grant num, #28/12 from the Al-Imam University, Riyadh, KSA.     

Positive solutions for critical quasilinear elliptic equations with mixed dirichlet-neumann boundary conditions

The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.