We study the existence of multiple nontrivial solutions for nonlinear fourth order discrete boundary value problems. first establish criteria at least two problems and obtain conditions to guarantee that are sign-changing. Under some appropriate assumptions, we further prove have three solutions, which positive, negative, sign-changing, respectively. include examples illustrate applicability ou...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented. c...

By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole “phase transition” of various gravitating systems. For the spherisymmetric real scalar field system, we find the “critical” spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear...

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdière, Gitler, and Vertigan, we characterize the circular planar graphs for which the inverse boundary value problem has a solution in this generalized non-linear setting. The answer is the same as in th...