相关论文: Optimal harvesting for a logistic model with grazi…

In this paper we prove existence, uniqueness of weak solutions of the following nonlocal nonlinear logistic equation \begin{equation*} \begin{cases} (-\Delta)_p^s u_\lambda=\lambda u_\lambda^q - b(x)u_\lambda^r \quad \text{in} \;\Omega,\\…

In this work we analyze the existence of solutions to the nonlinear elliptic system: \begin{equation*} \left\{ \begin{array}{rcll} -\Delta u & = & v^q+\a g & \text{in }\Omega , \\ -\Delta v& = &|\nabla u|^{p}+\l f &\text{in }\Omega , \\…

We construct positive singular solutions for the problem $-\Delta u=\lambda \exp (e^u)$ in $B_1\subset \mathbb{R}^n$ ($n\geq 3$), $u=0$ on $\partial B_1$, having a prescribed behaviour around the origin. Our study extends the one in Y.…

We prove existence and nonexistence results concerning elliptic problems whose basic model is \begin{equation*} \begin{cases} \displaystyle-\Delta u+\mu(x)\frac{|\nabla u|^2}{(u+\delta)^\gamma}= \lambda u^p, &x\in \Omega, \\ u> 0, &x\in…

We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large…

We investigate approximation guarantees provided by logistic regression for the fundamental problem of agnostic learning of homogeneous halfspaces. Previously, for a certain broad class of "well-behaved" distributions on the examples,…

Consider the Dirichlet problem with respect to an elliptic operator \[ A = - \sum_{k,l=1}^d \partial_k \, a_{kl} \, \partial_l - \sum_{k=1}^d \partial_k \, b_k + \sum_{k=1}^d c_k \, \partial_k + c_0 \] on a bounded Wiener regular open set…

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\J(u)=\int_{\partial\Omega} f(x) u \rd \H^{N-1}$ over some admissible class of…

We consider the problem of existence and uniqueness of strong solutions $u: \Omega \subset \mathbb{R}^n \longrightarrow \mathbb{R}^N$ in $(H^{2}\cap H^{1}_0)(\Omega)^N$ to the problem \[\label{1} \tag{1} \left\{ \begin{array}{l}…

We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…

We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of…

This paper deals with the existence and multiplicity of solutions for a class of Kirchhoff type elliptic system involving the Trudinger-Moser exponential growth nonlinearities. We first study the existence of solutions for the following…

In the paper, we consider the fractional elliptic system \begin{equation*}\left\{\begin{array}{ll} (- \Delta)^{\frac{\alpha_1}{2}}u(x)+\sum\limits^n_{i=1}b_i(x)\frac{\partial u}{\partial x_i}+B(x)u(x)=f(x,u,v),& \mbox { in } \Omega,\\ (-…

We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…

In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -\Delta u + \frac{|\nabla u|^2}{(1-u)^\gamma}=g & \mbox{in $\Omega$,}\newline \hfill u=0 \hfill & \mbox{on $\partial\Omega$,}…

We propose a new method for trajectory planning to solve the data harvesting problem. In a two-dimensional mission space, $N$ mobile agents are tasked with the collection of data generated at $M$ stationary sources and delivery to a base…

We study the behavior near the origin of $C^2$ positive solutions $u(x)$ and $v(x)$ of the system $0\leq -\Delta u\leq f(v)$ $0\leq -\Delta v\leq g(u)$ in $B_1(0)\backslash\{0\}$ where $f,g:(0,\infty)\to (0,\infty)$ are continuous…

We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality conditions for the optimal control of the total biomass…

We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which…

We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is $$\begin{cases} -\Delta_p u = H(u)\mu & \text{in}\ \Omega,\\ u>0…