Asymptotic behavior of ground state radial solutions for problems involving the \(\Phi \)-Laplacian

Abstract

We are concerned with the existence of positive solutions to the following boundary value problem in \((0,\infty ),\)

$$\begin{aligned} \frac{1}{A}\left( A\phi \left( \left| u^{\prime }\right| \right) u^{\prime }\right) ^{\prime }=-a(t)u^{\alpha },t>0,\left( A\phi \left( \left| u^{\prime }\right| \right) u^{\prime }\right) \left( 0\right) =0\text { and}\lim \nolimits _{t\rightarrow +\infty }u(t)=0, \end{aligned}$$

where \(\alpha \ge 0,\)\(\phi \) is a nonnegative continuously differentiable function on \(\left[ 0,\infty \right) \), A is a continuous function on \( \left[ 0,\infty \right) \), differentiable, positive on \(\left( 0,\infty \right) \) and a is a nonnegative function satisfying some appropriate assumptions related to Karamata regular variation theory. We give also, estimates on such solutions.

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Correspondence to Abdelwaheb Dhifli.

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Dhifli, A., Chemmam, R. & Masmoudi, S. Asymptotic behavior of ground state radial solutions for problems involving the \(\Phi \)-Laplacian. Positivity 24, 957–971 (2020). https://doi.org/10.1007/s11117-019-00715-y

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Keywords

  • Quasilinear elliptic equation
  • \(\Phi \)-Laplacian operator
  • Positive solutions
  • Asymptotic behaviour

Mathematics Subject Classification

  • 34B18
  • 35B40
  • 31C15