Existence of Solution for a p-Laplacian Multi-point Boundary Value Problem at Resonance

• Lin, Xiaojie ^[1] ; Zhang, Qin ^[1]
  1. [1] Jiangsu Normal Universit
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 143-154
• Idioma: inglés
• DOI: 10.1007/s12346-017-0259-7
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we are concerned with the p-Laplacian multi-point boundary value problem (ϕp(x′′(t)))′=f(t,x(t),x′(t),x′′(t)),t∈(0,1),ϕp(x′′(0))=∑i=1mαiϕp(x′′(ξi)),x′(1)=∑j=1nβjx′(ηj),x′′(1)=0,where ϕp(s)=|s|p-2s,p>1,ϕq=ϕp-1,1p+1q=1,f:[0,1]×R3→R is a continuous function, 0<ξ1<ξ2<⋯<ξm<1,αi∈R,i=1,2,…,m,m≥2 and 0<η1<⋯<ηn<1,βj∈R,j=1,…,n,n≥1. Based on the extension of Mawhin’s continuation theorem, a new general existence result of the p-Laplacian problem is established in the resonance case.

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