Differential equations and variational problems with variable exponent arise from the nonlinear elasticity theory and the theory of electrorheological fluids. This paper presents several sufficient conditions for the existence of at least one weak solution for the following boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions −|u′(x)|p(x)−2u′(x)′+α(x)|u(x)|p(x)−2u(x)=λf(x,u(x))in(0,1),|u′(0)|p(0)−2u′(0)=−λg(u(0)),|u′(1)|p(1)−2u′(1)=λh(u(1))where p∈C([0,1],R), f:[0,1]×R→R is a Carathéodory function, g,h:R→R are nonnegative continuous functions, λ>0, α∈L1([0,1]), with essinf[0,1]α>0. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.

Existence results for second-order boundary-value problems with variable exponents

Heidarkhani, Shapour
Primo
;
Barilla, David
Ultimo
2018

Abstract

Differential equations and variational problems with variable exponent arise from the nonlinear elasticity theory and the theory of electrorheological fluids. This paper presents several sufficient conditions for the existence of at least one weak solution for the following boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions −|u′(x)|p(x)−2u′(x)′+α(x)|u(x)|p(x)−2u(x)=λf(x,u(x))in(0,1),|u′(0)|p(0)−2u′(0)=−λg(u(0)),|u′(1)|p(1)−2u′(1)=λh(u(1))where p∈C([0,1],R), f:[0,1]×R→R is a Carathéodory function, g,h:R→R are nonnegative continuous functions, λ>0, α∈L1([0,1]), with essinf[0,1]α>0. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S1468121818303869-main.pdf

solo utenti autorizzati

Descrizione: Articolo
Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 721.1 kB
Formato Adobe PDF
721.1 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3172094
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact