On quadratic integral equations in Orlicz spaces
Copyright policy )On quadratic integral equations in Orlicz spaces
The existence of a nondecreasing solution \(x\) in an Orlicz space of the quadratic integral equation \[ x(t)=g(t)+\lambda x(t)\int_a^bK(t,s)f(s,x(s))ds \] is proved for sufficiently small \(\lambda\). By considering Orlicz spaces instead of \(L_p\) spaces, it is possible to consider functions \(f\) which grow faster than polynomials and rather singular kernels \(K\). For both situations corresponding results are described. The other hypotheses are monotonicity assumptions about \(f\), \(g\), and \(K\). The main tool for the proofs is an application of Darbo's fixed point theorem on a set of monotone functions.
- Damanhour University Egypt
- Adam Mickiewicz University in Poznań Poland
Other nonlinear integral equations, Monotonic solutions, quadratic integral equation, Applied Mathematics, Superposition operators, monotone solution, Orlicz spaces, Darbo's fixed point theorem, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc., nondecreasing solution, measure of noncompactness, Orlicz space, Integral equation, Analysis
Other nonlinear integral equations, Monotonic solutions, quadratic integral equation, Applied Mathematics, Superposition operators, monotone solution, Orlicz spaces, Darbo's fixed point theorem, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc., nondecreasing solution, measure of noncompactness, Orlicz space, Integral equation, Analysis
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