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Almost all weak solutions of the weighted p(.)-biharmonic problem

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Abstract

We give a new compact embedding theorem, and use an equivalent norm to obtain some different solutions of the weighted \(p\left( .\right) \)-biharmonic eigenvalue problem

$$\begin{aligned} \left\{ \begin{array}{cc} \Delta \left( \nu (x)\left| \Delta u\right| ^{p(x)-2}\Delta u\right) =\lambda \omega (x)\left| u\right| ^{q(x)-2}u, &{} \text {in }\Omega \\ u=\Delta u=0, &{} \text {on }\partial \Omega . \end{array} \right. \end{aligned}$$

Using Mountain Pass Theorem we show that the problem has a nontrivial weak solution. Moreover, we obtain infinite many pairs of solutions of the problem due to the Fountain Theorem.

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Authors and Affiliations

  1. Department of Mathematics, Sinop University, 57000, Sinop, Turkey

    Ismail Aydın

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Aydın, I. Almost all weak solutions of the weighted p(.)-biharmonic problem. J Anal 32, 171–190 (2024). https://doi.org/10.1007/s41478-023-00628-w

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