Some generalizations of the first Fredholm theorem to multivalued A-proper mappings with applications to nonlinear elliptic equations

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Let X and Y be real normed spaces with an admissible scheme Γ = {En, Vn; Fn, Wn} and T: X → 2Y A-proper with respect to Γ such that dist(y, A(x)) < kc(∥ x ∥) for all y in T(x) with ∥ x ∥ ≥ R for some R > 0 and k > 0, where c: R+ → R+ is a given function and A: X → 2Y a suitable possibly not A-proper mapping. Under the assumption that either T or A is odd or that (u, Kx) ≥ 0 for all u in T(x) with ∥ x ∥ ≥ r > 0 and some K: X → Y*, we obtain (in a constructive way) various generalizations of the first Fredholm theorem. The unique approximation-solvability results for the equation T(x) = f with T such that T(x) - T(y) ε{lunate} A(x - y) for x, y in X or T is Fréchet differentiable are also established. The abstract results for A-proper mappings are then applied to the (constructive) solvability of some boundary value problems for quasilinear elliptic equations. Some of our results include the results of Lasota, Lasota-Opial, Hess, Nečas, Petryshyn, and Babuška.

Original languageEnglish (US)
Pages (from-to)468-502
Number of pages35
JournalJournal of Mathematical Analysis and Applications
Volume65
Issue number2
DOIs
StatePublished - Sep 1978
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Some generalizations of the first Fredholm theorem to multivalued A-proper mappings with applications to nonlinear elliptic equations'. Together they form a unique fingerprint.

Cite this