We provide stability results for the family Lκu=∇Fκ(u) where Lκ is positive definite and selfadjoint operator and ∇Fκ for κ=0,1,2,... is a gradient mapping. The abstract results obtained are applied to prove the stability and continuous dependence on parameters for the fourth order Dirichlet problems for ordinary differential equations with the differential operator depending on numerical parameters.
We consider the fourth order periodic problem with a functional parameter. Some sufficient conditions under which solutions of this problem continuously depend on parameters are given. Proofs of theorems are based on variational methods.
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