Soliton solutions for quasilinear Schrödinger equations with critical growth

By João Marcos, Olimpio Hiroshi Miyagaki, Sérgio Henrique Monari Soares. 2010

201 citations recorded by the source corpus.

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/70949224eb63eb71ec3530ff3433912a3f1d1eae

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Quasilinear elliptic equations with critical growth via perturbation method (2013, methodology): “For example, one can choose R = α , α ∈ ( 4 , 2 ), as in [13].”
Quasilinear elliptic equations via perturbation method (2012, background): “…the ﬁrst attempt in this direction, though for the special form of equations (1), multiplicity results could be derived by using the change of variable arguments from [7, 11] (we refer to recent work [1, 8, 17] for more references on using the arguments of changing variables for various problems).”