Sobolev inequality of free boundary value problem for ( − 1 ) M ( d / d x ) 2 M

A 2 - D Free Boundary Value Problem with Onset ofa

Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...

ar X iv : c on d - m at / 9 60 50 76 v 1 1 2 M ay 1 99 6 Orbital Magnetism of 2 D Chaotic Lattices

We study the orbital magnetism of 2D lattices with chaotic motion of electrons withing a primitive cell. Using the temperature diagrammatic technique we evaluate the averaged value and rms fluctuation of magnetic response in the diffusive regime withing the model of non-interacting electrons. The fluctuations of magnetic susceptibility turn out to be large and at low temperature can be of the o...

The solution of M-D problem

Let p, q be any integer numbers greater that 1. We define the multiply-and-divide (M-D) sequence (an) for the multiplier p and divisor q recursively as follows. Begin with a1 = 1 and take an+1 equal to either ban/qc (bxc denotes floor of x, the largest integer not exceeding x) if this number is positive and has not yet occured in the sequence or pan otherwise. For instance, if p = 3 and q = 2, ...

TRIPLE SOLUTIONS FOR NONLINEAR SINGULAR m-POINT BOUNDARY VALUE PROBLEM

In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem  u′′(t) + βu(t) = h(t)f(t, u(t)), 0 < t < 1, u′(0) = 0, u(1) = m−2 ∑ i=1 αiu(ηi), where 0 < β < π2 , f ∈ C([0, 1] × R ,R). h(t) is allowed to be singular at t = 0 and t = 1. The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.