TY  - JOUR
AU  - Almutairi, Dalal
AU  - Ayed, Mohamed Ben
PY  - 2026
TI  - Boundary peak solutions with residual mass of a slightly subcritical Hénon type problem
JO  - AIMS Mathematics
SP  - 15324
EP  - 15360
VL  - 11
IS  - 6
AB  - We investigated the existence of boundary blow-up solutions for a slightly subcritical semilinear elliptic problem posed in a smooth bounded domain of              R        n   with    n  ∈  {  4  ,  5  ,  6  }. We constructed solutions that have a nonzero weak limit while simultaneously blowing up at a boundary point. This behavior stands in contrast to the well-known compactness properties on manifolds without boundary for small dimensions, where such weak convergence would force strong convergence. Our construction shows that, in low dimensions, the presence of a boundary allows blow-up and residual mass to coexist. Moreover, we identified the precise boundary points where this concentration occurs. The results are proved by means of delicate asymptotic estimates of the gradient of the associated Euler–Lagrange functional.
UR  - https://doi.org/10.3934/math.2026630
DO  - 10.3934/math.2026630