We consider the semilinear elliptic system { −∆u+m1(x)u = fu(x, u, v) x ∈ Ω, −∆v +m2(x)v = fv(x, u, v) x ∈ Ω, with the boundary conditions ∂u ∂n = λg(x, u) and ∂v ∂n = μh(x, v), where Ω ⊂ RN is a bounded smooth domain, λ, μ > 0 and the functions f , g, h, m1 and m2 satisfy some suitable conditions. Using the fibering map and by extracting the Palais-Smale sequences in the Nehari manifold, we pr...

We consider the two dimensional gravitational VlasovPoisson system. Using variational methods, we prove the existence of stationary solutions of minimal energy under a Casimir type constraint. The method also provides a stability criterion of these solutions for the evolution problem. Key-words. Vlasov-Poisson system – stellar dynamics – polytropic gas spheres – gravitation – mass – energy – ki...

Abstract. We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The problem arises from the aim to optimize the temperature gradient within crystal growth by the physical vapor transport (PVT) method. Based on a minimum...

Let be a bounded open subset of , function in Stummel classes where and
 semilinear monotone elliptic equation, is symmetric matrix, elliptic, bounded, and non decreasing Lipschitz. By proving weighted estimation for class with its weight which allows us to use Stampacchia’s lemma, we obtained the existence uniqueness solution this equation.

Reaction–diffusion systems are used to model many chemical and biological phenomena in the natural world [25, 26], and systems of coupled partial differential equations are also used in other physical models such as nonlinear Schrödinger systems in multi-component Bose–Einstein condensates and nonlinear optics [19, 23]. The steady-state solutions or standing-wave solutions of such systems of no...

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic 9 di$erential equations 3rst. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–di$usion 11 systems (non-Newtonian 3ltration systems) are establish...