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UDC 517.9 The paper deals with the existence and multiplicity of nontrivial weak solutions for the      (  x  )    -Kirchhoff-type problem,u  =  Δ  u  =  0  o  n  ∂  Ω  .By using variational approach and Krasnoselskii’s genus theory, we prove the existence and multiplicity of solutions for the      (  x  )    -Kirchhoff-type equation.

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On<mml:math><mml:mrow><mml:mi>𝓅</mml:mi><mml:mrow><mml:mo form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:mrow></mml:math>-Kirchhoff-type equation involving<mml:math><mml:mrow><mml:mi>𝓅</mml:mi><mml:mrow><mml:mo form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:mrow></mml:math>-biharmonic operator via genus theor

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