Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
Czasopismo
Rocznik
Tom
Strony
473--486
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Kraków, Poland, pawel.goncerz@im.uj.edu.pl
Bibliografia
- [1] G. Bonanno, P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian, Arch. Math. (Basel) 80 (2003), 424–429.
- [2] G. Bonanno, N. Giovanelli, An eigenvalue Dirichet problem involving the p-Laplacian with discontinuous nonlinearities, J. Math. Anal. Appl. 308 (2005), 596–604.
- [3] G. Bonanno, R. Livrea, Multiplicity theorems for the Dirichlet problem involving the p-Laplacian, Nonlinear Anal. 54 (2003), 1–7.
- [4] L. Gasinski, N.S. Papageorgiou, Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), 1091–1111.
- [5] L. Gasinski, N.S. Papageorgiou, Nodal and multiple constant sign solutions for resonant p-Laplacian equations with a nonsmooth potential, Nonlinear Anal. 71 (2009), 5747–5772.
- [6] L. Gasinski, N.S. Papageorgiou, On the existence of five nontrivial solutions for resonant problems with p-Laplacian, Discuss. Math. Differ. Incl. Control Optim. 30 (2010), 169–189.
- [7] L. Gasinski, N.S. Papageorgiou, Multiplicity of solutions for nonlinear elliptic equations with combined nonlinearities, [in:] Handbook of Nonconvex Analysis and Applications, D.Y. Gao and D. Motreanu (eds.), International Press, Boston, 183–262, 2010.
- [8] L. Gasinski, N. S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Chapman & Hall/CRC Press, Boca Raton, 2005.
- [9] Q. Liu, Existence of three solutions for p(x)-Laplacian equations, Nonlinear Anal. 68 (2008), 2119–2127.
- [10] S.A. Marano, D. Motreanu, On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems, Nonlinear Anal. 48 (2002), 37–52.
- [11] M. Mihailescu, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear Anal. 67 (2007), 1419–1425.
- [12] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65 (1986), AMS, Providence, RI.
- [13] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009), 3084–3089.
- [14] B. Ricceri, A further three critical points theorem, Nonlinear Anal. 71 (2009), 4151–4157.
- [15] B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problems, Math. Comput. Modelling 32 (2000), 1485–1494.
- [16] B. Ricceri, On a three critical points theorem, Arch. Math. (Basel) 75 (2000), 220–226.
- [17] D. Stancu-Dumitru, Two nontrivial solutions for a class of anisotropic variable exponent problems, Taiwanese Journal of Mathematics, in press.
- [18] L.-L.Wang, Y.-H. Fan, W.-G. Ge, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear Anal. 71 (2009), 4259–4270.
- [19] E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. III: Variational Methods and Optimization, Springer-Verlag, New York, 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHS-0004-0005