We survey some results about multiplicity of certain classes of entire solutions to semilinear elliptic equations or systems of the form −Δu=Fu(x,u), including the Allen Cahn or the stationary Nonlinear Schr"odinger case. In connection with this kind of problems we study some metric separation properties of sublevels of the functional V(u)=12‖∇u‖2H1(ℝN)−1p+1‖u‖p+1Lp+1(ℝN) in relation to the value of the exponent p+1∈(2,2∗N)
Gradient Lagrangian systems and semilinear PDE / Alessio, F. G.; Montecchiari, P.. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - STAMPA. - 3:6(2021). [10.3934/mine.2021044]
Gradient Lagrangian systems and semilinear PDE
F. G. Alessio;P. Montecchiari
2021-01-01
Abstract
We survey some results about multiplicity of certain classes of entire solutions to semilinear elliptic equations or systems of the form −Δu=Fu(x,u), including the Allen Cahn or the stationary Nonlinear Schr"odinger case. In connection with this kind of problems we study some metric separation properties of sublevels of the functional V(u)=12‖∇u‖2H1(ℝN)−1p+1‖u‖p+1Lp+1(ℝN) in relation to the value of the exponent p+1∈(2,2∗N)File in questo prodotto:
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