Ground state solutions for quasilinear Schrodinger equations with periodic potential
This article concerns the quasilinear Schrodinger equation $$\displaylines{ -\Delta u-u\Delta (u^2)+V(x)u=K(x)|u|^{2\cdot2^*-2}u+g(x,u),\quad x\in\mathbb{R}^N, \cr u\in H^1(\mathbb{R}^N),\quad u>0, }$$ where V and K are positive, continuous and periodic functions, g(x,u) is periodic in x...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/82/abstr.html |
| Summary: | This article concerns the quasilinear Schrodinger equation
$$\displaylines{
-\Delta u-u\Delta (u^2)+V(x)u=K(x)|u|^{2\cdot2^*-2}u+g(x,u),\quad x\in\mathbb{R}^N, \cr
u\in H^1(\mathbb{R}^N),\quad u>0,
}$$
where V and K are positive, continuous and periodic functions,
g(x,u) is periodic in x and has subcritical growth.
We use the generalized Nehari manifold approach developed by Szulkin and Weth
to study the ground state solution, i.e. the nontrivial solution with least
possible energy. |
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| ISSN: | 1072-6691 |