The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. We deduce that...

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.