In this paper, generalized boundary value problems for nonlinear fractional Langevin equations is studied. Some new existence results of solutions in the balls with different radius are obtained when the nonlinear term satisfies nonlinear Lipschitz and linear growth conditions. Finally, two examples are given to illustrate the results.

In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.

By using the theory of strongly continuous cosine families and the properties of completely continuous maps, we study the existence of mild, strong, classical and asymptotically almost periodic solutions for a functional second order abstract Cauchy problem with nonlocal conditions.

We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$\begin{array}{cc}\hfill {(-1)}^m{u}^{\left(2m\right)}\left(t\right)& =\lambda a\left(t\right)f\left(u\right(t\left)\right),0<t<1,\hfill \\ \hfill u^{\left(2i\right)}\left(0\right)& =u^{\left(2i\right)}\left(1\right)=0,i=0,1,2,\cdots ,m-1.\hfill \end{array}$$ where $a\in C\left(\right[0,1],[0,\infty \left)\right)$ and $a\left(t_0\right)>0$ for some $t_0\in [0,1]$, $f\in C\left(\right[0,\infty ),[0,\infty \left)\right)$ and $f\left(s\right)>0$ for $s>0$, and $f_0=\infty$, where $f_0={lim}_{s\to 0^{+}}f\left(s\right)/s$. We investigate the global structure of positive solutions by using Rabinowitz’s global bifurcation theorem.