Page 1

Displaying 1 – 2 of 2

Showing per page

Weak linking theorems and Schrödinger equations with critical Sobolev exponent

Martin Schechter, Wenming Zou (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation - Δ u + V ( x ) u = K ( x ) | u | 2 * - 2 u + g ( x , u ) , u W 1 , 2 ( 𝐑 N ) , where N 4 ; V , K , g are periodic in x j for 1 j N and 0 is in a gap of the spectrum of - Δ + V ; K > 0 . If 0 < g ( x , u ) u c | u | 2 * for an appropriate constant c , we show that this equation has a nontrivial solution.

Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent

Martin Schechter, Wenming Zou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation - Δ u + V ( x ) u = K ( x ) | u | 2 * - 2 u + g ( x , u ) , u W 1 , 2 ( 𝐑 N ) , where N ≥ 4; V,K,g are periodic in xj for 1 ≤ j ≤ N and 0 is in a gap of the spectrum of -Δ + V; K>0. If 0 < g ( x , u ) u c | u | 2 * for an appropriate constant c, we show that this equation has a nontrivial solution.

Currently displaying 1 – 2 of 2

Page 1