Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold
Copyright policy )Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold
Summary: We investigate the Kirchhoff type elliptic problem \[ \left(a+b\int_{\mathbb{R}^N} [|\nabla u|^2+V(x)u^2]\mathrm{d}x \right) [-\Delta u+V(x)u]=f(x,u), \quad x\in \mathbb{R}^N, \] where both \(V\) and \(f\) are periodic in \(x\), \(0\) belongs to a spectral gap of \(- \Delta +V\). Under suitable assumptions on \(V\) and \(f\) with more general conditions, we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.
Integro-partial differential equations, ground state solution, Quasilinear elliptic equations, Nehari-Pankov manifold, Kirchhoff equation, Critical points of functionals in context of PDEs (e.g., energy functionals), multiplicity of solutions
Integro-partial differential equations, ground state solution, Quasilinear elliptic equations, Nehari-Pankov manifold, Kirchhoff equation, Critical points of functionals in context of PDEs (e.g., energy functionals), multiplicity of solutions
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