Continuous dependence on function parameters for superlinear dirichlet problems
Tom 103 / 2005
Colloquium Mathematicum 103 (2005), 131-148
MSC: 35J20, 35J25.
DOI: 10.4064/cm103-1-14
Streszczenie
We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler–Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.
