Existence of positive solutions for a singular fractional boundary value problem

We study the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a sign-changing nonlinearity, subject to multi-point fractional boundary conditions

On a Liouville-type equation with sign-changing weight

In this paper we study the existence, non-existence and multiplicity of non-negative solutions for a family of elliptic problems with exponential nonlienarity and sign-changing weights. The techniques used in the proofs are a combination of upper and lower solutions, the Trudinger-Moser inequality and variational methods

Boundary changing operators in the O(n) matrix model

We continue the study of boundary operators in the dense O(n) model on the random lattice. The conformal dimension of boundary operators inserted between two JS boundaries of different weight is derived from the matrix model description. Our results are in agreement with the regular lattice findings. A connection is made between the loop equations in the continuum limit and the shift relations of boundary Liouville 3-points functions obtained from Boundary Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve