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...

In this paper, we are concerned with stable solutions to the fractional elliptic equation $$\begin{aligned} (-\Delta )^s u=e^u \text{ in } {\mathbb {R}}^{N}, \end{aligned}$$ where $$(-\Delta )^s$$ is Laplacian $$0<s<1$$ . By developing a new technique non-compactly supported test functions, establish nonexistence of provided that $$N<10s$$ This result optimal when $$s\uparrow 1$$ On other hand,...

Abstract. We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-norm is not sufficient for the exponential stability with respect to the C-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly ...

We study the nonlinearity of Exponential Welch Costas functions using the Fourier transform on Zn. Exponential Welch Costas functions are bijections from Zp−1 to Zp−1 defined using the exponential function of Zp, where p is an odd prime. Their linearity properties were recently studied by Drakakis, Requena, and McGuire, who conjectured that the absolute values of the Fourier coefficients of an ...