Unstable periodic solutions of a parabolic problem in the presence of non-well-ordered lower and upper solutions
The authors prove the solvability of the Dirichlet-periodic problem for a semilinear parabolic equation, assuming the existence of a lower solution \(\alpha\) and an upper solution \(\beta\) which do not satisfy the ordering condition \(\alpha\leq \beta\). The results yield the existence of unstable solutions, localized by means of \(\alpha\) and \(\beta\), requiring weak regularity of the coefficients of the equation.
scientific article; zbMATH DE number 1507745
scientific article