Nonnegative Solutions of Initial Value Problems for Langevin Equations Involving Two Fractional Orders
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DOI: 10.1007/s00009-018-1213-x
Abstract: In this paper, we study the existence and uniqueness of nonnegative solutions of an initial value problem for Langevin equations involving two fractional orders: $$\begin{aligned} \left\{ \begin{array}{lll}^c_0\!D^\beta _t({}^c_0\!D^\alpha _t-\gamma )x(t)=f(t,x(t)),&{}\quad \ 0< t read more here.
Keywords: solutions initial; initial value; nonnegative solutions; langevin equations ... See more keywords
Nonnegative solutions for the fractional Laplacian involving a nonlinearity with zeros
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DOI: 10.1007/s00229-021-01275-w
Abstract: We study the nonlocal nonlinear problem $$\begin{aligned} \left\{ \begin{array}[c]{lll} (-\Delta )^s u = \lambda f(u) &{} \text{ in } \Omega , \\ u=0&{}\text{ on } \mathbb {R}^N{\setminus }\Omega , \quad (P_{\lambda }) \end{array} \right. \end{aligned}$$… read more here.
Keywords: fractional laplacian; lambda lambda; solutions fractional; lambda ... See more keywords