Antonio J. Martinez Aparicio (Universidad de Almeria): Semilinear elliptic eigenvalue problems with infinitely many positive solutions




22/02/2024 at 14:30, Room 1B1, Building RM002

We study the behavior of the set of solutions of the semilinear elliptic problem -Δu = λf(u) in a bounded N-dimensional open set with Dirichlet boundary conditions. Here, f is a nonnegative continuous real function with multiple zeros. First, we analyze the set of the solutions whose maximum is between two consecutive positive zeros of f, arriving to the existence of an unbounded continuum of solutions with C-shape. Then, we study the asymptotic behavior of the countable many unbounded continua in the case in which f has a sequence of positive zeros, proving for some model cases that every λ>0 is a bifurcation point (either from infinity or from zero) that is not a branching point.

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