An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacain

Nonlinear Analysis, Theory, Methods and Applications

Volumn 58, Issue 3-4, 2004, Pages 477-488

  Ge, Weigao ^a   Ren, Jingli ^b  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b ZHENGZHOU UNIVERSITY   (China)

Author keywords

Boundary value problem; Continuation theorem; p Laplacian; Resonance

Indexed keywords

MATHEMATICAL OPERATORS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING; VECTORS;

BANACH SPACESS; CONTINUATION THEOREM; LINEAR SPACE; P-LAPLACIAN;

BOUNDARY VALUE PROBLEMS;

EID: 3042853406     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.01.007     Document Type: Article

References (14)

1. Przeradzki Bogdam, Stanczy Robert Solvability of a multi-point boundary value problem at resonance. J. Math. Anal. Appl. 264(2):2001;253-261.
2. p-2u′)′+f(t,u)=0,u(0)=t(T)=0,p>1 J. Differential Equations. 80(1):1989;1-3.
3. Feng W., Webb J.R.L. Solvability of three point boundary value problems at resonance. Nonlinear Anal. 30(6):1997;3227-3238.
4. Gaines R., Mawhin J. Coincidence Degree and Nonlinear Differential Equation. 1977;Springer, Berlin.
5. Garcia-Huidobro M., Manasevich R., Zanolin F. A Fredholm-like result for strongly nonlinear second order ODEs. J. Differential Equations. 114:1994;132-167.
6. Garcia-Huidobro M., Ubilla P. Multiplicity of solutions for a class of nonlinear second order equations. Nonlinear Anal. 28(9):1997;1509-1520.
7. Weigao Ge On the existence of harmonic solutions of Lienard system. Nonlinear Anal. 16(2):1991;183-190.
8. Gupta C.P. Solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation. J. Math. Anal. Appl. 168:1992;540-551.
9. Gupta C.P. A second order. M -point boundary value problem at resonance Nonlinear Anal. 24:1995;1483-1489.
10. Gupta C.P. A sharper condition for the solvability of a three point second order boundary value problem. J. Math. Anal. Appl. 205:1997;586-597.
11. Xiankai Huang, Zigui Xiang The. 2π -periodic solution of delay Duffing equation x″+g(t,x(t-τ))=p(t) Chinese Sci. Bull. 39(3):1994;201-203.
12. Karakostas G.L., Tsamatos P.Ch. On a nonlocal boundary value problem at resonance. J. Math. Anal. Appl. 259(1):2001;209-218.
13. Ma R. Positive solutions of a nonlinear three-point boundary value problem. Electronic J. Differential Equations. 1998(34):1998;1-8.
14. Weiping Sun, Weigao Ge The existence of solutions to Sturm-Liouville BVPs with Laplacian-like operator. Acta Math. Appl. Sinica. 18(2):2002;341-348.