كليدواژه :
Fourth , order equations , Variational methods , Infinitely many solutions
چكيده فارسي :
In this paper by using variational methods and critical point
theory, we obtain some sufficient conditions to guarantee that the
following problem has infinitely many classical solutions.
\begin{equation}\label{1.1}
\left\{\begin{array}{ll}
u^{(4)}(x)= \lambda h(x)k(u(x)) \ \ \ \mathrm{in}~~~ [0,1],\u(0)=u (0)=0,\u (1)=0,\qquad u (1)=\mu g(u(1)),
\end{array}\right.
\end{equation}
where $h\in L^1([0,1])$ such that $h(x)\geq 0$ a.e. $x\in [0,1]$,
$h\not\equiv 0,$ and $k:\mathbb{R}\rightarrow\mathbb{R}$ be a
nonnegative continuous function.
