Infinitely many solutions for some indefinite nonlinear elliptic problems.
Infinitely many solutions for some indefinite nonlinear elliptic problems.
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 \[ \begin{cases} -\Delta u= a(x)g(u)+ h(x)\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega.\end{cases}. \]
- University of Turin Italy
indefinite nonlinearities, contractibility of level sets, Nonlinear boundary value problems for linear elliptic equations, General existence and uniqueness theorems (PDE), semilinear elliptic boundary value problems, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
indefinite nonlinearities, contractibility of level sets, Nonlinear boundary value problems for linear elliptic equations, General existence and uniqueness theorems (PDE), semilinear elliptic boundary value problems, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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