Uniqueness criterion for solution of abstract nonlocal Cauchy problem

Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

Inhomogeneous Two-Parameter Abstract Cauchy Problem

existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

inhomogeneous two-parameter abstract cauchy problem

Unconditional Uniqueness of Solution for the Cauchy Problem of the Nonlinear Schrödinger Equation

where λ ∈ C and T > 0. Let α > 0 and s ≥ 0 be specified later, and let u0 ∈ H. Suppose that u ∈ C([0, T ];H) with (2) and u satisfies equation (1) in D0((0, T )× R), that is, in the distribution sense. We briefly recall known results on the uniqueness of solution for (1)-(2). In [3], Ginibre and Velo prove that if s = 1 and α < 4/(n− 2), the solution is unique. In [2], Cazenave and Weissler sho...