This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equation $left{begin{matrix} M(int_{Omega }frac{left | triangledownu right |^{p(x)}}{p(x)})(-Delta _{p(x)}u)=f(x,u), in nonfrenchspacingOmega , u=0,nonfrenchspacingonpartialOmega. end{matrix}right.$ Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M , we obtain results on existence and multiplicity of solutions.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equation $left{begin{matrix} M(int_{Omega }frac{left | triangledownu right |^{p(x)}}{p(x)})(-Delta _{p(x)}u)=f(x,u), in nonfrenchspacingOmega , u=0,nonfrenchspacingonpartialOmega. end{matrix}right.$ Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M , we obtain results on existence and multiplicity of solutions.
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Key Findings & Data:This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equation $left{begin{matrix} M(int_{Omega }frac{left | triangledownu right |^{p(x)}}{p(x)})(-Delta _{p(x)}u)=f(x,u), in nonfrenchspacingOmega , u=0,nonfrenchspacingonpartialOmega. end{matrix}right.$ Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M , we obtain results on existence and multiplicity of solutions.
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Conclusion & Impact:This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equation $left{begin{matrix} M(int_{Omega }frac{left | triangledownu right |^{p(x)}}{p(x)})(-Delta _{p(x)}u)=f(x,u), in nonfrenchspacingOmega , u=0,nonfrenchspacingonpartialOmega. end{matrix}right.$ Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M , we obtain results on existence and multiplicity of solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equation $left{begin{matrix} M(int_{Omega }frac{left | triangledownu right |^{p(x)}}{p(x)})(-Delta _{p(x)}u)=f(x,u), in nonfrenchspacingOmega , u=0,nonfrenchspacingonpartialOmega. end{matrix}right.$ Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M , we obtain results on existence and multiplicity of solutions.
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Cite This Article
AKKOYUNLU, E., AYAZOĞLU, R., AKBULUT, S. (2022). Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 4, 1342–1359. https://ajindex.com/articles/607273
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