Wojciech Kryszewski

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math.AP2016

The Bolzano mean-value theorem and partial differential equations

Wojciech Kryszewski, Jakub Siemianowski

We study the existence of solutions to abstract equations of the form $0 = A u + F (u)$ , $u \in K \subset E$ , where A is an abstract differential operator acting in a Banach space $E$ ,…

math.AP2016

Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term

Francisco Odair de Paiva, Wojciech Kryszewski, Andrzej Szulkin

We study the Schrödinger equations $- Δ u + V (x) u = f (x, u)$ in $R^{N}$ and $- Δ u - λ u = f (x, u)$ in a bounded domain $Ω \subset R^{N}$ . We assume that $f$ is superlinear bu…

math.AP2014

Bifurcation from infinity for an asymptotically linear Schrödinger equation

Wojciech Kryszewski, Andrzej Szulkin

We consider an asymptotically linear Schrödinger equation $- Δ u + V (x) u = λ u + f (x, u), x \in R^{N}$ , and show that if $λ_{0}$ is an isolated eigenvalue for the linearization at infinit…