Nonlinear Boundary Value Problems [chapter]

1974 Introduction to Singular Perturbations  
We consider the nonlinear Dirichlet problem −u ′′ − r(x)|u| σ u = λu in (0, ∞), u(0) = 0 and lim x→∞ u(x) = 0, and develop conditions for the function r such that the considered problem has a positive classical solution. Moreover, we present some results showing that λ = 0 is a bifurcation point in W 1,2 (0, ∞) and in L p (0, ∞) (2 ≤ p ≤ ∞).
doi:10.1016/b978-0-12-525950-7.50009-7 fatcat:eu55xzavvnhmppjhyrcso4alq4