A suggestion is put forward regarding a partial proof of casei which is elegant and simple enough to have caused Fermat's enthusiastic remark in the margin of his Bachet edition of Diophantus' . It is based on an extension of Fermat's Small Theorem () to mod for any 0, and the cubic roots of 1...

The nonlinear eigenvalue problem Δ+λ = 0 in the unit square with = 0 on the boundary is often referred to as “the Bratu problem” or “Bratu's problem.” The Bratu problem in 1-dimensional planar coordinates, ″ + λ = 0 with (0) = (1) = 0 has two known, bifurcated, exact solutions for...

Standard interpretations of Gödel's “undecidable” proposition, [∼(A)()], argue that, although [∼(A)()] is PA-provable if [(A)()] is PA-provable, we may not conclude from this that [∼(A)()] is PA-provable. We show that such interpretations are inconsistent with a standard Deduction...

In this paper we show the existence of a nontrivial solution for some elliptic problems in an Orlicz-Sobolev space setting with a sublinear right-hand side. We use the classical critical point theory with the Cerami (PS)-condition

The distribution of the number of points of the closed simple random walk, visited a given number of times (the -multiple point range) is analysed by a graph based approach. A general expression for the moments is derived. In this paper the joint generating function for dimension one is...

Investigation of the dependence of the eigenvalues on the domain is interesting from theoretical and practical points of view. In spite of actuality these investigations meet some difficulties related of first with the definition of the variation of the domain