[PDF] Top 20 On the existence of bounded solutions of nonlinear elliptic systems

... the nonlinear phenomena, such as the evo- lution of population, of chemical reaction, and so ...the existence of the solutions for a system of the ...the existence of the solutions for ... See full document

... Abstract. In this paper we study a class of nonvariational elliptic systems, by using the Gidas-Spruck Blow-up method. first, we obtain a priori estimates, and then using Leray-Schauder topological degree ... See full document

... the existence of weak solutions for the resonant elliptic problems, and then were widely used and extended (see [–] and their ...For nonlinear elliptic systems, let F s (x, s, ... See full document

... of nonlinear parabolic problems with p(x,t) growth ...the existence and uniqueness of bounded solutions to such a problem, with less constraint to ... See full document

... for nonlinear elliptic systems have received a lot of interest in recent years (see [–]), particularly when the nonlinear term appears as a source in the equa- tion, complemented with ... See full document

... where g(s) is singular at s = . They obtained similar results as that of []. Moreover, Boc- cardo and Orsina in [] discussed how the summability of f and the values of α affected the existence, regularity and ... See full document

... renormalized solutions, which was introduced by ...the existence of solutions of the Boltzmann equation, by introducing the idea of renormalized ... See full document

... the systems of singular elliptic equations with critical nonlinearities, various studies concerning the existence and multiplicity of nontrivial solutions have also been presented in the last ... See full document

... from nonlinear elasticity theory, electrorheo- logical fluids, ...weak solutions for differential equations with variable ...the existence of solutions for elliptic systems with ... See full document

... − div a(x, ∇ u) = Ᏺ(x,u), x ∈ R N , (1.1) where the operator div(a(x, ∇ u)) is nonlinear (and can be also degenerate), N ≥ 3 and function Ᏺ(x,u) satisfies several hypotheses. Our goal is to show how variational ... See full document

... inhomogeneous norm, and so it lacks the homogeneity property: kf |k|f. However, for nonlinear problems such as 1.3, the homogeneity property may not be an essential factor— we try to explain that the new space ... See full document

... To prove our results we adapt Mawhin’s continuation theorem in [2], and we give appropriate region for the system’s multiplicity by finding an a’priori bound.. To prove our assertion, we[r] ... See full document

... (See Lemma 2.3 for the proof of existence.) Let (u, v) be any solution, which exists by hypothesis, to (3.5) with a > h(0) and b = 0. Without loss of gen- erality, we will assume that a ≥ 1. We now show that h ... See full document

... the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary ... See full document

... the existence of the equilibrium solutions is established for the Volterra-Lotka mutualistic symbiosis model in the case of equal linear birth rates, using the method of upper and lower ... See full document

... the existence, uniqueness, stability, and continuity of solution p to the nonlinear equation ...the existence of weak solutions to Problem ... See full document

... semilinear elliptic differential equations on bounded domains, Brezis and Lieb [] obtained an existence result of solutions for a class of elliptic equations with critical Sobolev ... See full document

... Lakshmikantham, Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering, ...Positive Solutions of Operator Equations, Noordhoff, Groningen, ...the existence ... See full document

... the existence of periodic solutions for p-Laplacian elliptic systems, for example 21–24 ...periodic solutions for variable exponent systems are ...the existence of ... See full document

... As the potential V x and the nonlinearity f x, t are asymptotic to a constant function, Cao 10 obtained the existence of a nontrivial solution. As the potential V x and the nonlinearity fx, t are asymptotically ... See full document