Let 0 < q 1 p . In this study, we investigate positive solutions of the logistic elliptic equation − Δ u = ( ) in a smooth bounded domain Ω R N , ≥ with nonlinear boundary condition ∂ ν λ on This arises from coastal fishery harvesting. We prove that there exists at least one solution for every > case Furthermore, when is subcritical, exist two sufficiently small but no large enough Here, smalle...

This paper discusses flow control of fluids through porous media, specifically related to its application in petroleum science. The flow of fluids is described by the Boussinesq equation with mixed boundary conditions; a Neumann boundary condition describes no flow at the outer boundary of the porous media and a nonlinear boundary condition describes the interaction between the porous media and...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

In this paper suucient second order optimality conditions are established for optimal control problems governed by a linear elliptic equation with nonlinear boundary condition, where pointwise constraints on the control are given. The second order condition requires the coercivity of the Lagrange{function on a suitable subspace together with rst order suucient conditions on a certain set of str...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and nonlinear Neumann boundary condition. then construct sequence penalized PDEs, which converges to our initial problem. Since the we may be discontinuous, use notion solution in [Formula: see text]-viscosity sense. The method is based on backward stochastic their S-tightness. This work motiva...