We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in...

We study formation and interaction of one-dimensional screening solitons in a photorefractive medium with sublinear dependence of the photoconductivity on light intensity. We find an exact analytical solution to the corresponding nonlinear Schrodinger equation. We show that these solitons are stable in propagation and their interaction is generic for solitons of saturable nonlinearity. In parti...

Estimations of the number of solutions are given for various resonant cases of the boundary value problem x′′ + g(t, x) = f(t, x, x′), x(a) cos α − x′(a) sin α = 0, x(b) cos β − x′(b) sin β = 0, where g(t, x) is an asymptotically linear nonlinearity, and f is a sublinear one. We assume that there exists at least one solution to the BVP. 2000 Mathematics Subject Classification: 34B15.

in this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. we also generalize some known results for sublinear correspondences.