Instability and existence results to a non-autonomous two point boundary value problem
Abstract
We study the existence results and stability properties to the boundary value problem
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where λ > 0 is a parameter and f is a smooth function such that lim uniformly in x, f (x, −u)= − f (x, u) for x ∈ (−1, 1) and u > 0, and We use the method of sub-super solutions to establish our existence results and then we prove stability and instability of nontrivial nonnegative solutions under various choices of f.
Keywords
sub and supersolutions, linearized stability
