8 papers
Sublinear elliptic equations with a sharp change of sign in the nonlinearity
Mónica Clapp, Alberto Saldaña, Delia Schiera
We study the semilinear indefinite elliptic problem \[ -Δu = Q_Ω|u|^{p-2}u \quad \text{in } \mathbb{R}^N, \] where , …
On the asymptotically linear problem for an elliptic equation with an indefinite nonlinearity
Mónica Clapp, Cristian Morales-Encinos, Alberto Saldaña +1
We study the semilinear elliptic problem \[ -Δu = Q_Ω |u|^{p-2}u \quad \text{in } \mathbb{R}^N, \] where \( Q_Ω = χ_Ω - χ_{\mathbb{R}^N \setminus Ω} \) for a bounded smooth domain…
A concentration phenomenon for a semilinear Schrödinger equation with periodic self-focusing core
Mónica Clapp, Alberto Saldaña, Andrzej Szulkin
We consider the equation where takes the value on each ball , $y\in\mathbb…
Critical equations with a sharp change of sign in the nonlinearity
Mónica Clapp, Jorge Faya, Alberto Saldaña
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the va…
Multiple solutions to a semilinear elliptic equation with a sharp change of sign in the nonlinearity
Mónica Clapp, Angela Pistoia, Alberto Saldaña
We consider a nonautonomous semilinear elliptic problem where the power nonlinearity is multiplied by a discontinuous coefficient that equals one inside a bounded open set and…
On a Schrödinger system with shrinking regions of attraction
Mónica Clapp, Alberto Saldaña, Andrzej Szulkin
In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we es…
Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction
Mónica Clapp, Víctor Hernández-Santamaría, Alberto Saldaña
We study the existence and concentration of positive and nodal solutions to a Schrödinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suita…
Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system
Mónica Clapp, Alberto Saldaña, Mayra Soares +1
We establish the existence of a solution to a nonlinear competitive Schrödinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. Thi…