Asymptotic behavior of ground state radial solutions for \(p\)-Laplacian problems (Q355697)

The paper concerns the existence and uniqueness of positive solution to the following boundary value problem NEWLINE\[NEWLINE \frac{1}{A(x)}\left(A(x)\Phi_p\left(u^\prime\right)\right)^\prime+q(x)u^\alpha=0 \quad \text{in } (0,\infty),NEWLINE\]NEWLINE NEWLINE\[NEWLINE \lim_{x\rightarrow 0^+}A(x)\Phi_p\left(u^\prime\right)=0, \quad \lim_{x\rightarrow +\infty} u(x)=0, NEWLINE\]NEWLINE where \(A\in C([0,+\infty))\cap C^1 (0,+\infty)\) is positive in \((0,+\infty)\), \(\Phi_p(t)=t\left|t\right|^{p-2}\), \(p>1\), \(\alpha<p-1\) and \(q\) is a nonnegative continuous function on \((0,+\infty)\).