Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOLVABILITY OF NONLINEAR ELLIPTIC TYPE EQUATION WITH TWO UNRELATED NON STANDARD GROWTHS

  • Sert, Ugur (Faculty of Science Department of Mathematics Hacettepe University) ;
  • Soltanov, Kamal (Faculty of Science and Literature Department of Mathematics Igdir University)
  • Received : 2017.11.01
  • Accepted : 2018.05.11
  • Published : 2018.11.01
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Abstract

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths $$-div\({\mid}{\nabla}u{\mid}^{p_1(x)-2}{\nabla}u\)-\sum\limits^n_{i=1}D_i\({\mid}u{\mid}^{p_0(x)-2}D_iu\)+c(x,u)=h(x),\;{\in}{\Omega}$$ in a bounded domain ${\Omega}{\subset}{\mathbb{R}}^n$. Here, one of the operators in the sum is monotone and the other is weakly compact. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.

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References

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