Volume 12, Issue 1

The oracle c.c.c. is closely related to Cohen forcing. During an iteration we can “omit a type”; i.e. preserve “the intersection of a given family of Borel sets of reals is empty” provided that Cohen forcing satisfies it. We generalize this to other cases. In Section 1 we replace Cohen by “nicely” definable c.c.c., do the parallel of the oracle c.c.c. and end with a criterion for extracting a subforcing (not a complete subforcing, ) of a given nicely one and satisfying the oracle.

We study a mathematical problem describing the frictionless adhesive contact between an elastic body and a foundation. The adhesion process is modelled by a surface variable, the bonding field, and the contact is modelled with a normal compliance condition; the tangential shear due to the bonding field is included; the elastic constitutive law is assumed to be nonlinear and the process is quasistatic. The problem is formulated as a nonlinear system in which the unknowns are the displacement, the stress and the bonding field. The existence of a unique weak solution for the problem is established by using arguments for differential equations followed by the construction of an appropriate contraction mapping.

We study thermoplasticity with the Prandtl-Reuss flow rule and with a linear evolution equation for the kinematic hardening. The yield function associated with the system under consideration depends explicitly on the temperature. To have a control on the temperature, we slightly modify the heat equation and prove that an approximation process, based on the Yosida approximation, converges to a global in time solution of the (modified) system of thermoplasticity.

In this paper, by introducing some parameters and by employing a sharpening of Hölder's inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder's theorem is given.

We provide stability results for the family L k u = ∇ F k ( u ) where L k is a positive definite and selfadjoint operator and ∇ F k for k = 0, 1, 2, . . . is a gradient mapping. The abstract results obtained are applied to prove the stability and continuous dependence on parameters for the fourth order Dirichlet problems for ordinary differential equations with the differential operator depending on numerical parameters.

For ν > –1/2 and x real we shall establish explicit bounds for the Bessel function J ν ( x ) which are uniform in x and ν . This work and the recent result of L. J. Landau [J. Londom Math. Soc. 61: 197–215, 2000] provide relatively sharp inequalities for all real x .

In this paper, we prove existence results for singular problem Here the positive Carathédory function ƒ may be singular at the zero value of all its phase variables. Proofs are based on the Leray-Schauder degree and Vitali's convergence theorem.

The existence of at least one solution to a nonlinear second order differential equation in on the semi-infinite with the first derivative vanishing at infinity is proved by using topological methods. The second boundary condition is x (0) = 0 or x ′(0) = 0.

In the first part of this paper, we prove a minimax inequality for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part, a result on the existence of maximal element in non-compact domains is obtained and as application, we prove the existence of equilibrium for an abstract economy (or generalized game) with non-compact choice sets.

In this paper we characterize the products of four or more strong Świa̧tkowski functions.

We prove an existence theorem for the Darboux Problem u xy ( x, y ) = g ( u ( x, y )), u ( x , 0) = u (0, y ) = 0, where g is bounded and measurable.