For the p-Kirchhoff equation with prescribed L^p mass in R^3, the paper establishes the existence-nonexistence trichotomy, radial ground states and infinitely many high-energy solutions in the supercritical range, and convergence to the p-Laplacian limit as b approaches 0.
Normalized solutions of nonlinear Schr\"odinger equations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We consider the problem -\Delta u - g(u) = \lambda u, u \in H^1(\R^N), \int_{\R^N} u^2 = 1, \lambda\in\R, in dimension $N\ge2$. Here $g$ is a superlinear, subcritical, possibly nonhomogeneous, odd nonlinearity. We deal with the case where the associated functional is not bounded below on the $L^2$-unit sphere, and we show the existence of infinitely many solutions.
fields
math.AP 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Multiplicity and asymptotic behavior of normalized solutions to p-Kirchhoff equations
For the p-Kirchhoff equation with prescribed L^p mass in R^3, the paper establishes the existence-nonexistence trichotomy, radial ground states and infinitely many high-energy solutions in the supercritical range, and convergence to the p-Laplacian limit as b approaches 0.