Continuous dependence of solutions for indefinite semilinear elliptic problems
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2013
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We consider the superlinear elliptic problem
−∆u + m(x)u = a(x)u p
in a bounded smooth domain under Neumann boundary conditions, where
m ∈ L σ (Ω), σ ≥ N/2 and a ∈ C(Ω) is a sign changing function. Assuming
that the associated first eigenvalue of the operator −∆ + m is zero, we use
constrained minimization methods to study the existence of a positive solution
when m
b is a suitable perturbation of m.
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SILVA, Elves A. B.; SILVA, Maxwell L. Continuous dependence of solutions for indefinite semilinear elliptic problems. Electronic Journal of Differential Equations, San Marcos, v. 2013, n. 239, p. 1-17, 2013.