Semilinear elliptic problems on the half space with a supercritical nonlinearity.

Autor:	Katayama, Sho
Předmět:	BOUNDARY value problems SOBOLEV spaces BIFURCATION theory RADON EXPONENTS
Zdroj:	Discrete & Continuous Dynamical Systems: Series A; Dec2024, Vol. 44 Issue 12, p1-33, 33p
Abstrakt:	This paper concerns positive solutions to the boundary value problems of the scalar field equation in the half space with a Sobolev supercritical nonlinearity and an inhomogeneous Dirichlet boundary condition, admitting a nontrivial nonnegative Radon measure as the boundary data. Under a suitable integrability assumption on the boundary data and the Joseph–Lundgren subcritical condition on the nonlinear term, we give a complete classification of the existence/nonexistence of a positive solution with respect to the size of the boundary data. Furthermore, we give a result on the existence of multiple positive solutions via bifurcation theory. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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