[PDF] Top 20 1.On positive solution for a class of nonlinear elliptic systems with indefinite weights

... It is well known if J is bounded below and J has a minimizer on X , then this minimizer is a critical point of J. However, the Euler function J (u, v), associated with the problem (1.1), is not bounded below on the whole ... See full document

... “Multiple positive solutions for Dirichlet problems involving concave and convex nonlinearities,” Nonlinear Analysis: Theory, Methods & Applications, ...“Multiple positive solutions for ... See full document

... The first difficulty to be tackled in order to prove the existence of a solution for the system S is due to the fact that the preceding functional has a strong indefinite quadratic part. Therefore the ... See full document

... PC[0, 1], and using the well-known fixed point theorem of cone expansion and compression, we obtain conditions for the existence and multiplicity of positive solutions of system ...of positive ... See full document

... radial positive solutions vanishing at infinity for asymptotically homogeneous systems, Electronic ...54, 1-10.), we establish existence of nontrivial positive radial solution vanishing ... 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

... 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

... (0, 1), ω ≡ 0 on any open subinterval in (0, 1) which may be singular at t = 0 and/or t = ...of positive solution u λ on the parameter ... See full document

... a positive bounded function and f x g x     ,  C    are smooth functions which may change sign in ...multiple positive solutions to this equation is ve- ... See full document

... such systems have been paid great attention by many authors concerning existence, non- existence, multiplicity and qualitative ...The systems are to describe the interaction of nonlinear Schro- ... See full document

... When the nonlinear term just depends on u, the uniqueness of (1.2) has been exhaustively studied (see [1-6]). In 1985, the uniqueness of (1.2) was discussed in dif- ferent domains by Ni and Nussbaum [7] to ... See full document

... a positive ra- dial solution u ∗ of system ...a solution u ∗ with u ∗ i ≥ 0 (i = 1, 2, ...= 1, 2, ...thus positive in Ω = { x ∈ R n : R 1 < | x | < R 2 , R 1 ... See full document

... of positive solutions for equations and sys- tems of equations related to Dirichlet problems have been studied in several papers during the last ...for systems involving the p-Laplacian operator in general ... See full document

... In Section 2, we obtain some results on the nonlinear term F. In Section 3, we approach the variational method and recall the critical point theorem which is the linking theorem for the strongly indefinite ... See full document

... Lakshmikantham, Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering, ...Krasnosel’ski˘ı, Positive Solutions of Operator Equations, Noordhoff, Groningen, ...of ... 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

... The following sections are organized as follows. In Sect. 2, some useful lemmas and notations are given. In Sect. 3, sufficient conditions are established for the existence of positive periodic solutions of (1.1). ... See full document

... quasilinear elliptic equation div  |  u | m  2  u  = ( ) ( ) p x f u  q x g u ( ) ( ) are established, where m  2 , f and g are nondecreasing and vanish at the ... See full document

... − u pr−2 u |u| qr−2 u C, r ∈ 0, 1, 1.8 because of the nonhomogeneity of pt-Laplacian, when we use critical point theory to deal with the existence of solutions, we usually need the corresponding functional is ... See full document

... W 1,px 1–5 have been a subject of active research stimulated mainly by the development of the studies of problems in elasticity, electrorheological fluids, image processing, flow in porous media, calculus ... See full document