Open AccessSOLUTIONS OF A NONLINEAR DIRICHLET PROBLEM IN WHICH THE NONLINEAR PART IS BOUNDED FROM ABOVE AND BELOW BY POLYNOMIALS
Author(s) -
Jan Beczek
Publication year - 1997
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1997.9637064
Subject(s) - bounded function , injective function , multiplicity (mathematics) , mathematics , nonlinear system , continuous function (set theory) , domain (mathematical analysis) , dirichlet problem , combinatorics , function (biology) , pure mathematics , discrete mathematics , mathematical analysis , physics , boundary value problem , quantum mechanics , evolutionary biology , biology
In this paper we study the existence and multiplicity solutions of nonlinear elliptic problem of the formHere Ω is a smooth and bounded domain in RN , N ≥ 2, λ ∈ R and f : R → R is a continuous, even function satisfying the following conditionfor some c 1, c 2, c 3, p, α ∈ R, c 1, c 2, c 3, α > 0 and p > 1+ α.We shall show that, for λ ∈ R, g ∈ Lr (Ω) if N = 2, r > 1, p > 1 + α or the above problem has solutions.Assuming additionally that, λ ≤ λ1 and f is decreasing for t ≤ 0, we shall show that, this problem have exctly one solution.We take advantage of the fact, that a continuous, proper and odd (injective) map of the form I + C (where C is compact) is suriective (a homeomorphism).