[PDF] Top 20 Positive solutions for a class of sublinear elliptic systems

... We are interested in the existence of positive solutions of (.) under weaker assump- tions. More concretely, we consider the existence of positive solutions of (.) from the following two ... See full document

... Let u(t,a) denote the unique solution of Equation 2.1. If a > 0, then the solution u(t, a) is positive for t slightly larger than a. When it vanishes in (a, b), we define b(a) to be the first zero of u(t, a ). ... See full document

... In recent years, there has been considerable progress on the study of semipositione problems (F (0) < 0 but finite)(see [2],[3],[6]). Many results have been obtained on kind of infinite semipositone problems; see for ... See full document

... Existence and concentration of positive solutions for P ∗ have been extensively studied in the recent years; see, for example, Ambrosetti et al. 2, 3, Cingolani and Lazzo 4, 5, Floer and Weinstein 6, Oh ... See full document

... variational structure. Up to now, the tools to study (.) are a fixed point result with Leray- Schauder condition and the Schaefer fixed point theorem. Very recently, Alves and Covei [] established the sub-supersolution ... See full document

... [2] F. Cìrstea and V. Rădulescu, “Entire Solutions Blowing up at Infinity for Semilinear Elliptic Systems,” Journal de Mathématiques Pures et Appliquées, Vol. 81, No. 9, 2002, pp. 827-846. ... See full document

... of positive solutions to sublinear semilinear el- liptic systems with two equations have been recently studied in ...The sublinear con- dition plays an important ...a positive ... See full document

... reaction-diffusion systems that appear in chemical and biological phe- nomena, including the steady and unsteady state situation (see [–]), has been extensively investigated in recent ...multiple ... See full document

... Zhang, “Existence of positive solutions for elliptic systems with nonstandard px-growth conditions via sub-supersolution method,” Nonlinear Analysis: Theory, Methods & Applications, vol.[r] ... See full document

... On the p(x)-Laplacian problems, maybe the first eigenvalue and the first eigenfunc- tion of p(x)-Laplacian do not exist. Even if the first eigenfunction of p(x)-Laplacian exist, because of the nonhomogeneity of ... See full document

... Kato class, hence they cannot be regarded as the lower order perturbation ...Schrödinger-Poisson systems in R  , [] for singular elliptic systems in R  , and [] for large singular ... See full document

... symmetric solutions for very general f (see ...many positive nonradial solutions of the above problem for some f (see ...tiple positive entire solutions for a class of f , ... See full document

... two solutions for problem () under the condition that f is sublinear at infinity by using saddle point ...two solutions for problem () by using of the saddle point theorem and Galerkin approx- ... See full document

... radial positive solutions vanishing at infinity for asymptotically homogeneous systems, Electronic ...nontrivial positive radial solution vanishing at infinity, namely “ground states”, under the ... See full document

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

... Varga, Variational Principles in Mathematical Physics, Geom- etry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems , Encyclopedia of Mathematics and it[r] ... See full document

... two solutions for a more general nonlinearity g(·, ...nontrivial solutions and four non- trivial solutions by a similar variational approach, depending on the position of a suitable parameter with ... See full document

... of positive solutions for general nonlinear elliptic equations and systems, and that numerous related works are devoted to some of its variants, such as more general quasilinear operators, and ... See full document

... multiplicity solutions for a class of sublinear fourth-order elliptic equation of Kirchhoff type by using the genus properties in critical ... See full document

... div |∇v| q − 2 ∇v = n |x| u β , x ∈ R N , (1.4) where α > 0, β > 0, p > 1, and q > 1. As far as the author knows, there are no results that contain existence criteria of entire explosive positive ... See full document