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A Dirichlet problem with asymptotically linear and changing sign nonlinearity. (English) Zbl 1086.35048

The authors discuss the existence of positive solutions to the problem \[ -\Delta u= g(x, u),\quad u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^d\), \(g(x,s)\) is allowed to change sign and has an asymptotically linear behaviour in \(\delta\) at infinity. Using the mountain pass theorem the authors prove existence of solutions for (1).

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
47J30 Variational methods involving nonlinear operators
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