A priori estimates for a semilinear elliptic system without variational structure and their applications

Notions of sublinearity and superlinearity for nonvariational elliptic systems

“…We already explained in the introduction that if D is positive definite then D satisfies (17). We are going to prove the converse.…”

“…To prove (a) let for instance i = n and suppose for contradiction that there exists U ′ ∈ R n−1 \ {0}, such that U ≥ 0 and D nn U ≤ 0. Then the vector U = (U ′ , 0) violates (17). We are going to prove (b) and (c) through an induction with respect to n. …”

“…A priori bounds for general systems of type (P 0 ) were obtained by Nussbaum [14], but they require quite restrictive growth hypotheses on the nonlinearities. We refer also to [17] and to the forthcoming paper [8], where much sharper a priori estimates for systems of two equations are established. Remark 2.…”

Solvability of boundary value problems for second order impulsive differential equations on whole line with a non-Carathédory nonlinearity

“…Lane-Emden equations arise naturally from the study of various nonlinear phenomena, such as pattern formation, population evolution, chemical reaction and has attracted considerable attention in recent years [27,29,34].…”

Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System

“…Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as: pattern formation; population evolution; chemical reactions; and so on (see for example [22]) and have attracted much attention in recent years. Several authors have established existence and uniqueness results for the Lane-Emden systems [23,24] and other related systems (see e.g., [25][26][27] and references therein).…”