Solvability of p,q-Laplacian systems with potential boundary conditions

Abstract

Existence results to boundary value problems for non-potential p, q-Laplacian systems with potential boundary conditions are established. The approach relies on Schaefer fixed point theorem, combined with a technique involving matrices convergent to zero.

Authors

Petru Jebelean
Department of Mathematics, West University of Timişoara, Timişoara, Romania

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

p-Laplacian; subdifferential;  uniform non-resonance; Sxhaefer fixed point theorem;  matrix convergent to zero.

Paper coordinates

P. Jebelean, R. Precup, Solvability of p,q-Laplacian systems with potential boundary conditions, Appl. Anal. 89 (2010), 221-228, https://doi.org/10.1080/00036810902889567

PDF

??

About this paper

Journal
Applicable Anaysis An International Journal
Publisher Name

Taylor and Francis

Print ISSN

0003-6811

Online ISSN

1563-504X

google scholar link

[1] Gasinski, L and Papageorgiou, NS. 2003. Nonlinear second-order multivalued boundary value problems. Proc. Indian Acad. Sci. (Math. Sci.), 113: 293–319.  [Google Scholar]
[2]
Jebelean, P. 2008. Variational methods for ordinary p-Laplacian systems with potential boundary conditions. Adv. Diff. Eqns, 13: 273–322.  [Google Scholar]
[3]
Jebelean, P. 2008. Infinitely many solutions for ordinary p-Laplacian systems with non-linear boundary conditions. Comm. Pure Appl. Anal., 7: 267–275.  [Google Scholar]
[4]
Jebelean, P and Moroşanu, G. 2006. Ordinary p-Laplacian systems with non-linear boundary conditions. J. Math. Anal. Appl., 313: 738–753.  [Crossref], [Web of Science ®], [Google Scholar]
[5]
Granas, A and Dugundji, J. 2003. Fixed Point Theory, New York: Springer.  [Crossref], [Google Scholar]
[6]
Couchouron, J-F and Precup, R. 2007. Homotopy method for positive solutions of p-Laplace inclusions. Topol. Methods Nonlin. Anal., 30: 157–169.  [Google Scholar]
[7]
Precup, R. 2009. The role of matrices that are convergent to zero in the study of semilinear operator systems. Math. Comput. Modelling, 49: 703–708.  [Crossref], [Web of Science ®], [Google Scholar]
[8]
Muzsi, D and Precup, R. 2008. Nonresonance and existence for systems of non-linear operator equations. Applicable Anal., 87: 1005–1018.  [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[9]
Precup, R. 2002. Methods in Nonlinear Integral Equations, Dordrecht: Kluwer.  [Crossref], [Google Scholar]
[10]
Dincă, G and Jebelean, P. 2008. A priori estimates for the vector p-Laplacian with potential boundary conditions. Arch. Math., 90: 60–69.  [Google Scholar]

2010

Related Posts