We consider an elliptic equation −∆u + u = 0 with nonlinear boundary conditions ∂u ∂n = λu + g(λ, x, u), where g(λ, x, s) s → 0, as |s| → ∞. In [1, 2] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or… (More)
In this paper we study a reduced continuous model describing the local evolution of high grade gliomas-a lethal type of primary brain tumor-through the interplay of different cellular phenotypes. We show how hypoxic events, even sporadic and/or limited in space may have a crucial role on the acceleration of the growth speed of high grade gliomas. Our… (More)
We consider the elliptic equation −u+u = 0 with nonlinear boundary conditions ∂ u/∂n = λu + g(λ, x, u), where the nonlinear term g is oscillatory and satisfies g(λ, x, s)/s → 0 as |s| → 0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero.