The existing methods have been unable to prove the existence of multi-peak solutions to the p-Laplace equation
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The existing methods have been unable to prove the existence of multi-peak solutions to the p-Laplace equation. The Liapunov-Schmidt reduction is not applicable in this case.
Evidence profile
Sourced from the stated research gap of the source papers, classified as general, spanning 3 journals. Those papers have been cited 1 times in total.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- A New Minimax Principle and Application to the p-Laplace Equation (2026) · Archive for Rational Mechanics and Analysis · doi
The existing methods have been unable to prove the existence of multi-peak solutions to the p-Laplace equation. The Liapunov-Schmidt reduction is not applicable in this case.
generalstated research gapevidence 5/5Keywords: existing methods have been unable prove existence multi-peak - On the stability of the critical p-Laplace equation (2026) · Journal of Functional Analysis · cited 1× · doi
The paper identifies a gap in the existing literature on the critical p-Laplace equation, namely the lack of an optimal stability result for non-negative solutions. The paper notes that previous work has established the existence and uniqueness of solutions, but the stability of the solutions is still an open question.
generalstated research gapevidence 5/5Keywords: paper identifies gap existing literature critical p-laplace equation - On Rayleigh quotients connected to p-Laplace equations with polynomial nonlinearities (2026) · Journal of Differential Equations · doi
The paper identifies a gap in prior work as the lack of a detailed analysis of the bijection between normalized critical points of Rα and solutions of the p-Laplace equations for different relations between p, q, r. The authors argue that prior work has not provided a comprehensive study of the properties of Rα.
generalstated research gapevidence 5/5Keywords: paper identifies gap prior work lack detailed analysis
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