Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian

被引：10

作者：

Aydin, Ismail ^{[1
]}

Unal, Cihan ^{[2
]}

机构：

[1] Sinop Univ, Fac Arts & Sci, Dept Math, Sinop, Turkey

[2] Select Placement Ctr, Republ Turkey, Ankara, Turkey

来源：

RICERCHE DI MATEMATICA | 2023年 / 72卷 / 02期

关键词：

Weak solution; p(.)-Laplacian; Mountain Pass Lemma; Fountain Theorem; Ekeland variational principle; EXPONENT SOBOLEV SPACES; SMOOTH FUNCTIONS; DENSITY; C(INFINITY)(0)(R-N);

D O I：

10.1007/s11587-021-00621-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By applying Mountain Pass Lemma, Ekeland's variational principle and Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem {-div(a(x) vertical bar del u vertical bar(p(x)-2) del u) =lambda b(x)vertical bar u vertical bar(q(x)-2) u, x is an element of Omega a(x) vertical bar del u vertical bar(p(x)-2) partial derivative u/partial derivative u + beta(x)vertical bar u vertical bar(p(x)-2) u = 0, x is an element of partial derivative Omega, under some appropriate conditions in the space W-a,b(1, p(.)) (Omega).

引用

页码：511 / 528

页数：18

共 35 条

[1] Robin problems involving the p(x)-Laplacian [J].

Allaoui, Mostafa .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 332 :457-468

[2]

Aydin I, 2020, IN PRESS

[3] THREE SOLUTIONS TO A STEKLOV PROBLEM INVOLVING THE WEIGHTED p(.)-LAPLACIAN [J].

Aydin, Ismail ;

Unal, Cihan .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2021, 51 (01) :67-76

[4] Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth [J].

Aydin, Ismail ;

Unal, Cihan .

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2020, 49 (04) :1383-1396

[5] The Kolmogorov-Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces [J].

Aydin, Ismail ;

Unal, Cihan .

COLLECTANEA MATHEMATICA, 2020, 71 (03) :349-367

[6] Weighted Variable Sobolev Spaces and Capacity [J].

Aydin, Ismail .

JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2012,

[7]

Ciarlet PG., 2013, LINEAR NONLINEAR FUN

[8] Eigenvalues of the p(x)-Laplacian Steklov problem [J].

Deng, Shao-Gao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (02) :925-937

[9] Positive solutions for Robin problem involving the p(x)-Laplacian [J].

Deng, Shao-Gao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (02) :548-560

[10] A local mountain pass theorem and applications to a double perturbed p(x)-Laplacian equations [J].

Deng, Shao-Gao .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 211 (01) :234-241

← 1 2 3 4 →