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Infinitely many solutions for some indefinite nonlinear elliptic problems. (English) Zbl 0949.35051

Summary: We prove the existence of infinitely many solutions of nonlinear elliptic boundary value problems with indefinite (i.e. changing sign) nonlinearities. In our problem the nonlinearity is also non-symmetric. The symmetry is perturbed by a term \(h\in L^2(\Omega)\), i.e. we consider the problem \[ \begin{cases} -\Delta u= a(x)g(u)+ h(x)\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega.\end{cases}. \]

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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