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...

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is...

Abstract In this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get theorems via variational methods and corresponding two-critical-point theorems. Combining with Newton-iterative method, an example presented to illustrate value obtained

This paper aims to establish the existence of a weak solution for non-local problem: \begin{equation*} \left\{\begin{array}{ll} -a\left(\int_{\Omega}\mathcal{H}(x,|\nabla u|)dx \right) \Delta_{\mathcal{H}}u &=f(x,u) \ \hbox{in} \Omega, \\ \hspace{3.3cm} u &= 0 \hbox{on} \partial \end{array}\right. \end{equation*} where $\Omega\subseteq \mathbb{R}^{N},\, N\geq 2$ is bounded and smooth domain con...