Two solutions for nonhomogeneous Klein-Gordon equations coupled with Born-Infeld type equations
DOI:
https://doi.org/10.58997/ejde.2022.74Keywords:
Klein-Gordon equation; Born-Infeld theory; nonhomogeneous; Mountain pass theorem; Ekeland's variational principle.Abstract
This article concerns the nonhomogeneous Klein-Gordon equation coupled with a Born-Infeld type equation,
$$\displaylines{- \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u)+h(x), \quad x\in \mathbb{R}^3,\cr \Delta \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \quad x\in \mathbb{R}^3, }$$ where \(\omega\) is a positive constant. We obtain the existence of two solutions using the Mountain Pass Theorem, and the Ekeland's variational principle in critical point theory.
For more information see https://ejde.math.txstate.edu/Volumes/2022/74/abstr.html
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