Existence of Sign‐Changing Solutions to Equations Involving the One‐Dimensional p‐Laplacian

Ruyun Ma and Lingfang Jiang

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: We consider the equations involving the one‐dimensional p‐Laplacian (P): (u′tp-2u′(t)) ′+λf(u(t))=0, 0 100,λ>,f∈C1(R;R),f(s)s>, and s ≠ 0. We show the existence of sign‐changing solutions under the assumptions f∞ = lim|s|→∞⁡(f(s)/sp−1) = +∞ and f0 = lim|s|→0(f(s)/sp−1)∈[0, ∞]. We also show that (P) has exactly one solution having specified nodal properties for λ ∈ (0, λ*) for some λ* ∈ (0, ∞). Our main results are based on quadrature method.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/810193

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:810193

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().