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 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
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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Bu Makaleye Atıf Yap
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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