Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity
Copyright policy )Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity
This paper is devoted to study semilinear elliptic boundary value problem, that is; \[ -\Delta u=f(u)\quad\text{in }\Omega, \qquad u|_{\partial\Omega}=0, \tag{1} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb R^n\). The authors compute that critical groups of zero and infinity to get a nontrivial solution. Using the Fučik spectrum, the ordinary differential equation theory of Banach spaces and Morse theory, they obtain new existence results for nontrivial solutions for (1), multiple solutions and sign-changing solutions.
- Chinese Academy of Sciences China (People's Republic of)
- Academy of Mathematics and Systems Science China (People's Republic of)
multiple solutions, Nonlinear boundary value problems for linear elliptic equations, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, critical groups of zero, Morse theory, Nonlinear elliptic equations, sign-changing solutions
multiple solutions, Nonlinear boundary value problems for linear elliptic equations, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, critical groups of zero, Morse theory, Nonlinear elliptic equations, sign-changing solutions
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