Abstract
We study a nonlinear q(m)-Kirchhoff-type problems under Dirichlet boundary condition with nonlocal terms and logarithmic nonlinearity, in the setting of "variable exponents" Sobolev spaces in compact Riemannian manifolds. Using the Mountain Pass Theorem, the Fountain and Dual Fountain Theorem, we discuss the existence and multiplicity of three notions of solutions: nontrivial weak solutions, large energy solutions and small negative energy solutions. One of the main difficulties and innovations of the present paper is the presence of nonlocal terms and logarithmic nonlinearity. Our results extend and generalize some recent works in the existing literature.
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Communicated by Maria Alessandra Ragusa.
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Bouaam, H., El Ouaarabi, M., Allalou, C. et al. Variable exponent q(m)-Kirchhoff-type problems with nonlocal terms and logarithmic nonlinearity on compact Riemannian manifolds. Bull. Malays. Math. Sci. Soc. 46, 97 (2023). https://doi.org/10.1007/s40840-023-01498-y
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DOI: https://doi.org/10.1007/s40840-023-01498-y
Keywords
- Compact Riemannian manifolds
- Nonlocal terms
- Logarithmic nonlinearity
- Mountain Pass theorem
- Fountain and Dual Fountain Theorem