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Existence and multiplicity of stationary solutions for a Cahn--Hilliard-type equation in $\mathbb{R}^N$

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  • Solutions of the stationary semilinear Cahn--Hilliard-type equation $$ -\Delta^2 u - u -\Delta(|u|^{p-1}u)=0 \quad \mbox{in}     \mathbb{R}^N, \quad \mbox{with} \quad p>1, $$ which are exponentially decaying at infinity, are studied. Using the Mounting Pass Theorem allows us the determination of two different solutions. On the other hand, the application of Lusternik--Schnirel'man (L--S) Category Theory shows the existence of, at least, a countable family of solutions.
    Mathematics Subject Classification: Primary: 35G20, 35K52.

    Citation:

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