Semilinear elliptic Schrödinger equations with singular potentials and absorption terms

GKIKAS, Konstantinos T. and Phuoc-Tai NGUYEN. Semilinear elliptic Schrödinger equations with singular potentials and absorption terms. Journal of the London Mathematical Society. Wiley, 2024, vol. 109, No 1, p. 1-53. ISSN 0024-6107. Available from: https://dx.doi.org/10.1112/jlms.12844.

Basic information

• Original name: Semilinear elliptic Schrödinger equations with singular potentials and absorption terms
• Authors: GKIKAS, Konstantinos T. and Phuoc-Tai NGUYEN (704 Viet Nam, guarantor, belonging to the institution).
• Edition: Journal of the London Mathematical Society, Wiley, 2024, 0024-6107.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.200 in 2022
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1112/jlms.12844
• UT WoS: 001157209900010
• Keywords in English: Hardy potentials; Critical exponents; Source terms; Capacities; Measure data
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

Let Ω⊂RN (N≥3) be a C2 bounded domain and Σ⊂Ω be a compact, C2 submanifold without boundary, of dimension k with 0≤k1, we show that problem (P) admits several critical exponents in the sense that singular solutions exist in the subcritical cases (i.e. p is smaller than a critical exponent) and singularities are removable in the supercritical cases (i.e. p is greater than a critical exponent). Finally, we establish various necessary and sufficient conditions expressed in terms of appropriate capacities for the solvability of (P).

Links

• GA22-17403S, research and development project: Name: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem (Acronym: NSESSP)

Investor: Czech Science Foundation