# Multibump solutions for quasilinear elliptic equations with critical growth

@article{Liu2013MultibumpSF, title={Multibump solutions for quasilinear elliptic equations with critical growth}, author={Jiaquan Liu and Zhi-Qiang Wang and Xian Wu}, journal={Journal of Mathematical Physics}, year={2013}, volume={54}, pages={121501} }

The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrodinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct…

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## References

SHOWING 1-10 OF 49 REFERENCES

### Ground states for quasilinear Schrödinger equations with critical growth

- Mathematics
- 2013

For a class of quasilinear Schrödinger equations with critical exponent we establish the existence of both one-sign and nodal ground states of soliton type solutions by the Nehari method. The method…

### Nash moser methods for the solution of quasilinear schrödinger equations

- Mathematics
- 1999

Using new Nash Moser techniques for Frechet spaces by M. Poppenberg the local existence, uniqueness and continuous dependence of smooth solutions of a special quasilinear evolutionary Schrodinger…

### EXISTENCE OF WEAK SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN

- Mathematics
- 2008

This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation − ` ∆pu + ∆p(u ) ́ + V (x)|u|p−2u = h(u) in RN . Here V is a positive continuous potential bounded…

### Multiple solutions for quasilinear Schrödinger equations involving critical exponent

- MathematicsAppl. Math. Comput.
- 2010

### A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

- Mathematics
- 2006