A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function

AbstractIn this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (Eλ,μ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of R2

Existence and multiplicity of positive solutions for a Schrodinger-Poisson system with a perturbation

In this paper we study the nonlinear Schrodinger-Poisson system with a perturbation: \begin{equation*} \begin{cases} -\Delta u+u+K( x) \phi u=\vert u\vert ^{p-2}u+\lambda f(x)\vert u\vert ^{q-2}u \text{in }\mathbb{R}^{3}, -\Delta \phi =K( x) u^{2} \text{in }\mathbb{R}^{3}, \end{cases} \end{equation*}% where $K$ and $f$ are nonnegative functions, $2\ge q\leq p\le 6$ and $p\ge 4$, and the parameter $\lambda \in \mathbb{R}$. Under some suitable assumptions on $K$ and $f$, the criteria of existence and multiplicity of positive solutions are established by means of the Lusternik-Schnirelmann category and minimax method

Symmetry and concentration behavior of ground state in axially symmetric domains

We let Ω(r) be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation in Ω(r) are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground-state solutions

Normalized solutions for the Schr\"{o}dinger equation with combined Hartree type and power nonlinearities

We investigate normalized solutions for the Schr\"{o}dinger equation with combined Hartree type and power nonlinearities, namely \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+\lambda u=\gamma (I_{\alpha }\ast \left\vert u\right\vert ^{p})|u|^{p-2}u+\mu |u|^{q-2}u & \quad \text{in}\quad \mathbb{R}^{N}, \\ \int_{\mathbb{R}^{N}}|u|^{2}dx=c, & \end{array}% \right. \end{equation*} where $N\geq 2$ and $c>0$ is a given real number. Under different assumptions on $\gamma ,\mu ,p$ and $q$, we prove several nonexistence, existence and multiplicity results. In particular, we are more interested in the cases when the competing effect of Hartree type and power nonlinearities happens, i.e. $\gamma \mu <0,$ including the cases $\gamma 0$ and Due to the different "strength" of two types of nonlinearities, we find some differences in results and in the geometry of the corresponding functionals between these two cases

Improve Production Process Performance By Using Lean Management －A Case Study of Lady Underwear

People around the world work every year to improve the requirement standards of various commodities. Product life cycles are getting shorter, replaced by a number of innovative products; thus, in order to adapt to social changes, companies must develop a number of innovative products to attract consumers to buy. In Taiwan, most development occurs in small and medium traditional industries. Women’s underwear is a personal privacy product. As women are gradually being taken more seriously, women’s underwear products are gradually increasing in value, but the women’s underwear and underwear fabric design process is quite complex and time-consuming. To help enterprises improve production performance, this study introduces lean enterprise management, using IE tools for program analysis, which provides time to study the law, and 7S management practices, identifies problems, and proposes ways to improve in order to verify the practices and analysis of results. Research pointed out that introducing lean management for enterprises to improve process performance, so that women’s underwear product processes achieve significant improvement, improved results as follows: Before and after the improvement, GAP reached 23.83%; product production time was reduced; employee take line operation time reduced; quantization benefits of $1,909,425 improved the efficiency to$1,023,225, putting the cost at $106,200; and table bad rate increased the cost by$780,000. These results show that in the present study, lean management practices successfully improved the production performance of the women’s underwear industry included in this study. It is expected that the process improvements can provide a method for the lingerie industry to continuously improve and succeed in raising the performance feedback of employees to increase cohesion so that the company reaps more profits and benefits