Strongly Nonlinear Integral Equations of Hammerstein Type
AUTOR(ES)
Browder, Felix E.
RESUMO
This paper studies the solution of the nonlinear Hammerstein equation u(x) + ʃ k(x,y)f[y,u(y)]μ(dy) = h(x) in the singular case, i.e., where the linear operator K with kernel k(x,y) is not defined for all the range of the nonlinear mapping F given by Fu(y) = f[y,u(y)] over the whole class X of functions u which are potential solutions of the equation. An existence theorem is derived under relatively minimal assumptions upon k and f, namely that (Ku,u) ≥ 0, that K maps L1 into L1loc and is compact from L1 [unk] L∞ into L1loc, that f(y,s) has the same sign as s for ǀsǀ ≥ R, and that for each constant r > 0, ǀf(y,s)ǀ ≤ gr(y) for ǀsǀ ≤ r where g is bounded and summable. The proof is obtained by combining a priori bounds, a truncation procedure, and a convergence argument using the Dunford-Pettis theorem.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=432663Documentos Relacionados
- Degree of mapping for nonlinear mappings of monotone type: Strongly nonlinear mapping
- A NEW APPROACH TO THE NUMERICAL SOLUTION OF A CLASS OF LINEAR AND NONLINEAR INTEGRAL EQUATIONS OF FREDHOLM TYPE*
- ON SOME NONLINEAR INTEGRAL EQUATIONS OCCURRING IN THE THEORY OF DYNAMIC PROGRAMMING
- Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
- Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind