Photo from archive.org
Abstract We consider quasilinear Schrodinger equations in R N of the form − Δ u + V ( x ) u − u Δ ( u 2 ) = g… Click to show full abstract
Abstract We consider quasilinear Schrodinger equations in R N of the form − Δ u + V ( x ) u − u Δ ( u 2 ) = g ( u ) , where g ( u ) is 4-superlinear. Unlike all known results in the literature, the Schrodinger operator − Δ + V is allowed to be indefinite, hence the variational functional does not satisfy the mountain pass geometry. By a local linking argument and Morse theory, we obtain a nontrivial solution for the problem. In case that g is odd, we get an unbounded sequence of solutions.
Keywords:
dinger equations;
waves quasilinear;
equations indefinite;
quasilinear schr;
standing waves;
schr dinger
Journal Title: Journal of Differential Equations
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Journal of Differential Equations
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!