Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

• Autorzy: Gasiński L. , Papageorgiou N. S.
• Języki publikacji: EN

Abstrakty

EN

We consider a nonlinear Neumann elliptic equation driven by the p-Laplacian and a Caratheodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.

Słowa kluczowe

EN

Palais-Smale condition; noncoercive functional; second deformation theorem

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2012
• Tom: Vol. 21
• Strony: 27--40
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Gasiński L.

• Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

autor

Papageorgiou N. S.

• Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Bibliografia

• [1] Anello G.; Existence of infinitely many weak solutions for a Neumann problem, Non-linear Anal. 57, 2004, pp. 199-209.
• [2] Bartolo P., Benci V., Fortunato D.; Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity, Nonlinear Anal. 7, 1983, pp. 981-1012.
• [3] Filippakis M., Gasiński L., Papageorgiou N.S.; Multiplicity result for nonlinear Neumann problems, Canad. J. Math. 58, 2006, pp. 64-92.
• [4] Gasiński L., Papageorgiou N.S.; Nonlinear Analysis, Chapman and Hall/CRC Press, Boca Raton, FL, 2006.
• [5] Lieberman G.M.; Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12, 1988, pp. 1203-1219.
• [6] Motreanu D., Papageorgiou N.S.; Existence and multiplicity of solutions for Neumann problems, J. Differential Equations 232, 2007, pp. 1-35.
• [7] O'Regan D., Papageorgiou N.S.; The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem, Nonlinear Anal. 70, 2009, pp. 4386-4392.
• [8] Wu X.-P., Tan K.K.; On existence and multiplicity of solutions of Neumann boundary value problems for quasi-linear elliptic equations, Nonlinear Anal. 65, 2006, pp. 1334-1347.