SOME RESULTS ON INDEFINITE SUBLINEAR ELLIPTIC RADIAL PROBLEMS WITH SIMULTANEOUS DIRICHLET AND NEUMANN BOUNDARY CONDITIONS

Abstract

Abstract Let B be a ball in R N $\mathbb {R}^{N}$ double struck upper R Superscript upper N , N ≥ 1 $N\geq 1$ upper N greater than or equals 1 , let m ∈ C ( B ― ) $m\in C(\overline {B}) $ m element of upper C left parenthesis upper B overbar right parenthesis be a radial function that changes sign in B and let 0 < q < 1 $0 0 less than q less than 1 . We consider the existence and nonexistence of (nontrivial) nonnegative solutions and positive solutions for semilinear elliptic problems of the form − Δ u = m ( x ) u q $-\Delta u=m( x) u^{q}$ minus normal upper Delta u equals m left parenthesis x right parenthesis u Superscript q in B , u = ∂ ν u = 0 $u=\partial _{\nu }u=0$ u equals partial differential Subscript nu Baseline u equals 0 on ∂ B $\partial B$ partial differential upper B

The authors' abstract, as published at the source. Bulletin of the Australian Mathematical Society, 2026 · DOI ↗