Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)

Francesco Tulone, Valeria Iiritano

Risultato della ricerca: Article

Abstract

Let be a bounded smooth domain in . We prove a general existence result of least energy solutions and least energy nodal ones for the problem where f is a Carathéodory function. Our result includes some previous results related to special cases of f. Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type , with and .
Lingua originaleEnglish
pagine (da-a)303-314
Numero di pagine12
RivistaComplex Variables and Elliptic Equations
Volume63
Stato di pubblicazionePublished - 2018

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Least Energy Solutions
Dirichlet Problem
Nehari Manifold
Carathéodory Function
Global Minimum
Energy Functional
Existence Results
Nonlinearity
Restriction
Energy

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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abstract = "Let be a bounded smooth domain in . We prove a general existence result of least energy solutions and least energy nodal ones for the problem where f is a Carath{\'e}odory function. Our result includes some previous results related to special cases of f. Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type , with and .",
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T1 - Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)

AU - Tulone, Francesco

AU - Iiritano, Valeria

PY - 2018

Y1 - 2018

N2 - Let be a bounded smooth domain in . We prove a general existence result of least energy solutions and least energy nodal ones for the problem where f is a Carathéodory function. Our result includes some previous results related to special cases of f. Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type , with and .

AB - Let be a bounded smooth domain in . We prove a general existence result of least energy solutions and least energy nodal ones for the problem where f is a Carathéodory function. Our result includes some previous results related to special cases of f. Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type , with and .

UR - http://hdl.handle.net/10447/236480

UR - http://www.tandfonline.com/doi/full/10.1080/17476933.2017.1307346

M3 - Article

VL - 63

SP - 303

EP - 314

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

ER -