In this paper, we study the asymptotic behavior of solutions to Kirchhoff type stochastic plate equation driven by additive noise defined on unbounded domains. We first prove uniform estimates and then establish existence upper semicontinuity random attractors.

We study the following singular Kirchhoff type problem 
 \[\left( P\right) \left\{
 \begin{array} [c]{c}
 -m\left({\displaystyle\int\limits_{\Omega}}\left\vert \nabla u\right\vert ^{2}dx\right) \Delta u=h\left( u\right)
 \frac{e^{\alpha u^{2}}}{\left\vert x\right\vert ^{\beta}}\text{ \ in} \Omega,\\
 u=0 \text{on}\; \partial\Omega
 \end{array} \right.
 \]&#x0D...

In this article, we deal with the existence of non-negative solutions class following non local problem $$ \left \{ \textstyle\begin{array}{l} \quad - M\left (\displaystyle \int _{\mathbb{R}^{n}}\int _{\mathbb{R}^{n}} \frac{|u(x)-u(y)|^{\frac{n}{s}}}{|x-y|^{2n}}~dxdy\right ) (-\Delta )^{s}_{n/s} u=\left _{\Omega }\frac{G(y,u)}{|x-y|^{\mu }}~dy \right )g(x,u) \; \text{in}\; \Omega , \\ u =0\quad...

Abstract In this paper, we study a class of ( p , q )-Schrödinger–Kirchhoff type equations involving continuous positive potential satisfying del Pino–Felmer conditions and nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques Lusternik–Schnirelman category theory, relate the number solutions topology set where attains its minimum values.

The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.