Hamiltonian elliptic system involving nonlinearities with supercritical exponential growth by Yony Raúl Santaria Leuyacc

“…In this paper, we deal with the existence of nontrivial solutions to the following class of strongly coupled Hamiltonian systems: $ \begin{equation*} \quad \left\{ \begin{array}{rclll} -{\rm div} \big(w(x)\nabla u\big) \ = \ g(x,v),&\ & x \in B_1(0), \\[5pt] - {\rm div}\big(w(x) \nabla v\big)\ = \ f(x,u),&\ & x \in B_1(0), \\[5pt] u = v = 0&\ & x \in \partial B_1(0), \end{array} \right. …”
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Global behavior of a max-type system of difference equations of the second order with four variables and period-two parameters by Taixiang Sun, Guangwang Su, Bin Qin, Caihong Han

“…<p>In this paper, we study global behavior of the following max-type system of difference equations of the second order with four variables and period-two parameters</p> <p class="disp_formula">$ \left\{\begin{array}{ll}x_{n} = \max\Big\{A_n , \frac{z_{n-1}}{y_{n-2}}\Big\}, \ y_{n} = \max \Big\{B_n, \frac{w_{n-1}}{x_{n-2}}\Big\}, \ z_{n} = \max\Big\{C_n , \frac{x_{n-1}}{w_{n-2}}\Big\}, \ w_{n} = \max \Big\{D_n, \frac{y_{n-1}}{z_{n-2}}\Big\}, \ \end{array}\right. \ \ n\in \{0, 1, 2, \cdots\}, $</p> <p>where $ A_n, B_n, C_n, D_n\in (0, +\infty) $ are periodic sequences with period 2 and the initial values $ x_{-i}, y_{-i}, z_{-i}, w_{-i}\in (0, +\infty)\ (1\leq i\leq 2) $. …”
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