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Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity. (English) Zbl 1198.35118
Summary: By an application of Bonanno’s three critical point theorem, we establish the existence of a nontrivial solution to the problem
\[ \begin{aligned} -\Delta_p u= \mu \frac{g(x)|u|^{p-2}u}{|x|^p} +\lambda a(x)f(u) &\quad \text{in }\Omega,\\ u =0 &\quad \text{on }\partial \Omega, \end{aligned} \]
under some restrictions on \(g,a\) and \(f\) for certain positive values of \(\mu\) and \(\lambda\).

MSC:
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J75 Singular elliptic equations
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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