### Abstract

The nonexistence of positive solutions is discussed for -△_{p}u = a(x)u^{q-1} in Ω, u|∂Ωn = 0, for the case where a(x) is a bounded positive function and Ω is a strip-like domain such as Ω = Ω_{d} x ℝ^{N-d} with Ω_{d} bounded in ℝ^{d}. The existence of nontrivial solution of (E) is proved by Schindler for q ∈ (p,p*) where p* is Sobolev's critical exponent. Our method of proofs for nonexistence rely on the "Pohozaev-type inequality" (for q ≥ p*); and on a new argument concerning the simplicity of the first eigenvalue for (generalized) eigenvalue problems combined with translation invariance of the domain (for q ≤ p).

Original language | English |
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Pages (from-to) | 565-578 |

Number of pages | 14 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 3 |

Issue number | 4 |

Publication status | Published - 1997 |

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics
- Discrete Mathematics and Combinatorics

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## Cite this

Hashimoto, T., & Otani, M. (1997). Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains.

*Discrete and Continuous Dynamical Systems*,*3*(4), 565-578.