WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
Behavior of Entire Solutions of a Nonlinear Elliptic Equation with An Inhomogeneous Singular Term
Authors: ,
Abstract: In this paper, we are interested in the singular positive solutions of the inhomogeneous radial equation $$(|u'|^{p-2}u')' (r)+\frac{N-1}{r}|u'|^{p-2}u'(r)+u^{q}(r)+f(r)=0, r>0$$, where $$N \geq 1, p > 2, q > 1$$ and $$f$$ is a continuous radial and strictly positive function on $$(0, +\infty)$$. More precisely, we study the solutions $$u$$ that cannot be extended by continuity at zero, that is, $$\lim_{r \rightarrow 0}u(r)= +\infty$$. We give existence and nonexistence results and we describe the behavior of entire solutions near infinity. The
study needs some assumptions on $$p, q, N$$ and explicit conditions on the inhomogeneous term $$f$$.
Search Articles
Keywords: Inhomogeneous elliptic equation, entire solutions, strictly positive solutions, energy function, asymptotic behavior near infinity.
Pages: 232-244
DOI: 10.37394/23206.2023.22.28