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A note on the dependence of solutions on functional parameters for nonlinear Sturm-Liouville problems

Orpel A.

Opuscula Mathematica

2014

Vol. 34, no. 4

837--849

We deal with the existence and the continuous dependence of solutions on functional parameters for boundary valued problems containing the Sturm-Liouville equation. We apply these result to prove the existence of at least one solution for a certain class of optimal control problems.

Continuous dependence of solutions of elliptic BVPs on parameters

Orpel A.

Opuscula Mathematica

2006

Vol. 26, no. 2

351-359

The continuous dependence of solutions for a certain class of elliptic PDE on functional parameters is studied in this paper. The main result is as follow: the sequence {k}k∈N of solutions of the Dirichlet problem discussed here (corresponding to parameters {uk}k∈N) converges weakly to x0 (corresponding to u0) in W1,q 0 (Ω, R), provided that {uk}k∈N tends to u0 a.e. in Ω. Our investigation covers both sub and superlinear cases. We apply this result to some optimal control problems.