On a class of double phase problem with nonlinear boundary conditions

Liyan Wang; Jihong Shen; Kun Chi; Bin Ge; Liyan Wang; Jihong Shen; Kun Chi; Bin Ge

doi:10.3934/era.2023019

Electronic Research Archive

2023, Volume 31, Issue 1: 386-400. doi: 10.3934/era.2023019

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On a class of double phase problem with nonlinear boundary conditions

Liyan Wang ¹,
Jihong Shen ^{1,2
,
,},
Kun Chi ¹,
Bin Ge ^{1,2
,
,}

1.
College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, China
2.
College of Mathematical Sciences, Harbin Engineering University, Harbin, China

Received: 19 September 2022 Revised: 28 October 2022 Accepted: 28 October 2022 Published: 04 November 2022

The existence of nontrivial solutions of the double phase problem with nonlinear boundary value condition is an important quasilinear problem: we use variational techniques and sum decomposition of a space $ W_0^{1, \xi}(\Omega) $ to prove the existence of infinitely many solutions of the problem considered. Moreover, our conditions are suitable and different from those considered previously.
- double phase problem,
- nonlinear boundary condition,
- variational method,
- infinitely many solutions,
- sign-changing potential
Citation: Liyan Wang, Jihong Shen, Kun Chi, Bin Ge. On a class of double phase problem with nonlinear boundary conditions[J]. Electronic Research Archive, 2023, 31(1): 386-400. doi: 10.3934/era.2023019

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Abstract

The existence of nontrivial solutions of the double phase problem with nonlinear boundary value condition is an important quasilinear problem: we use variational techniques and sum decomposition of a space $ W_0^{1, \xi}(\Omega) $ to prove the existence of infinitely many solutions of the problem considered. Moreover, our conditions are suitable and different from those considered previously.

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