In this paper we study a nonlinear elliptic differential equation driven by thep-Laplacian with a multivalued boundary condition of the Neumann type. Using techniques from the theory of maximal monotone operators and a theorem of the range of the sum of monotone operators, we prove the existence of a (strong) solution.
1991 Mathematica Subject Classification
Key words and phrases
Neumann problems maximal monotone operators subdifferentials boundedly inversely compact equality in the sense of distributions trace maps and spaces
This is a preview of subscription content, log in to check access.
Dal Maso G.,An Introduction to Γ-Convergence, Birkhäuser, Boston, 1993.Google Scholar
Del Pino M., Elgueta M., Manasevich R.,A homotopic deformation along p of a Leray-Schauder degree result and existence for (|u′|p−2u′)′+f(t,u)=0, u(0)=u(T)=0, p>1, J. Diff. Eqns.,80 (1983), 1–13.Google Scholar
Diaz J. I.,Nonlinear Partial Differential Equations and Free Boundaries I: Elliptic Equations, Research Notes in Math., no. 106, Pitman, London, 1985.MATHGoogle Scholar
Drabek P.,Solvability of boundary value problems with homogeneous ordinary differential operator, Rendiconti dell'Istituto Matematico, Trieste,6 (1985), 105–124.Google Scholar
Hachimi A. El., Gossez J. P.,A note on a nonresonant condition for a quasilinear elliptic problem, Nonl. Anal.,22 (1994), 229–236.MATHCrossRefGoogle Scholar
Guo Z.,Boundary value problems of a class of quasilinear ordinary differential equations, Diff. Integ. Eqns.,6 (1993), 705–719.MATHGoogle Scholar
Gupta C., Hess P.,Existence theorems for nonlinear noncoercive operators and nonlinear elliptic boundary value problems, J. Diff. Eqns.,22 (1976), 305–313.MATHCrossRefMathSciNetGoogle Scholar