## Classical and weak solutions of a singular semilinear elliptic problem.(English)Zbl 0880.35043

Authors’ summary: The singular semilinear elliptic equation $$\Delta u+p(x)f(u)= 0$$ is shown to have a unique positive classical solution in $$\mathbb{R}^n$$ that decays to zero at $$\infty$$ if $$p(x)$$ is simply a nontrivial nonnegative continuous function satisfying $$\int^\infty_0 t(\max_{|x|=t}p(x))dt<\infty$$, provided $$f$$ is a nonincreasing continuously differentiable function on $$(0,\infty)$$. It is also shown that the equation has a unique weak $$H^1_0$$-solution on a bounded domain provided $$\int^\varepsilon_0 f(s)ds<\infty$$ and $$p(x)\in L^2$$.

### MSC:

 35J60 Nonlinear elliptic equations

### Keywords:

unique positive classical solution
Full Text:

### References:

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