Keywords: Discrete Homological nontrivial critical point Morse theory Local linking a b s t r a c t In this paper, the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem (BVP) ÀD 2 uðk À 1Þ ¼ kf ðk; uðkÞÞ k 2 þ is a parameter. By using the critical point theory and Morse theory, we obtain that the above (BVP) has solutions fo...

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method. Keywords—Discrete boundary value problems, nonsmooth critical point theory, positive solutions, semipositone, sub-super solutions method

We point out that the permanent confinement in a compact 2+1-dimensional U(1) Abelian Higgs model is destroyed by matter fields in the fundamental representation. The deconfinement transition is Kosterlitz-Thouless like. The dual theory is shown to describe a three-dimensional gas of point charges with logarithmic interactions which arises from an anomalous dimension of the gauge field caused b...

where τ, σ , and c are constants in R with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T(> 0)-periodic function in t > 0, and for an arbitrary bounded domain E ⊂ R, g(t,x) is a Lipschitz function in [0,T] × E, p ∈ C(R,R), p(t +T) = p(t), and ∫ T 0 p(t)dt = 0. They obtained some sufficient conditions to guarantee the existence, at least a T-periodic solution, for this system. But, for the existence of pe...