Extremal solutions for nonlinear neumann problems
Copyright policy )Extremal solutions for nonlinear neumann problems
The authors investigate the Neumann problem in a smooth bounded domain for the equation \[ -\text{ div } \left(\|\nabla x\|^{p-2}\nabla x \right) = f(\cdot,x,\nabla x) \] with usual regularity and growth conditions on \(f\). Assuming the existence of upper and lower solutions the authors show that the set of solutions is nonvoid and directed and thus (by Zorn's lemma) contains a maximal and a minimal solution.
- University of Urbino Italy
- University of Rome Tor Vergata Italy
lower solution, Upper solution, lower solution, order interval, truncation function, penalty function, pseudomonotone operator, coercive operator, extremal solution., pseudomonotone operator, upper solution, Nonlinear boundary value problems for linear elliptic equations, nonlinear Neumann problem, Nonlinear elliptic equations, extremal solution, \(p\)-Laplacian
lower solution, Upper solution, lower solution, order interval, truncation function, penalty function, pseudomonotone operator, coercive operator, extremal solution., pseudomonotone operator, upper solution, Nonlinear boundary value problems for linear elliptic equations, nonlinear Neumann problem, Nonlinear elliptic equations, extremal solution, \(p\)-Laplacian
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