What question did this study set out to answer?

To establish the existence of a normalized solution for a quasilinear elliptic problem with general potentials.

April 1, 2026Journal of Fixed Point Theory and Applications0 citationsOpen Access

Normalized solution for quasilinear Schrödinger operators with general potentials: the Lᵖ-supercritical case

OMO. H. Miyagaki ESEdcarlos Domingos da Silva CGC. Goulart

Key Points

To establish the existence of a normalized solution for a quasilinear elliptic problem with general potentials.
Formulated a quasilinear elliptic equation involving Schrödinger operators.
Applied variational techniques to show the existence of solutions.
Considered suitable functions within the Sobolev space W^{1, p}(R^N).
Demonstrated that solutions exist under specific conditions for parameters N, p, and q.
Proved that solutions satisfy the normalization constraint with respect to L^p norms.

Abstract

Abstract We establish the existence of a normalized solution for the following quasilinear elliptic problem: aligned \ array{cc - ₚ u + V (x) |u|^p-2u = |u|^p - 2u + | u| ^q-2u\ in\ RN, \\ ₑN |u|ᵖ dx = mᵖ, \ u W^1, p (RN), array. aligned - Δ p u + V (x) | u | p - 2 u = λ | u | p - 2 u + u q - 2 u in R N, ∫ R N | u | p d x = m p, u ∈ W 1, p (R N), where N > p N > p, 1< p< p+ p²N< q < p^* <mml: math xmlns: mml="http: //www. w3. org/1998/Math/Mat

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