Existence of Positive Solutions for a Class of px, qx-Laplacian Elliptic Systems with Multiplication of Two Separate Functions

The paper deals with the study of the existence of weak positive solutions for a new class of the system of elliptic differential equations with respect to the symmetry conditions and the right hand side which has been defined as multiplication of two separate functions by using the sub-supersolutions method (1991 Mathematics Subject Classification: 35J60, 35B30, and 35B40).

[1]  Qihu Zhang,et al.  Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems , 2009 .

[2]  Yasutaka Sibuya,et al.  Über die Differentialgleichung y″ = f(x, y, y′) , 1993 .

[3]  Takeshi Kura.  The weak supersolution-subsolution method for second order quasilinear elliptic equations , 1989 .

[4]  Salah Boulaaras.  Some existence results for a new class of elliptic Kirchhoff equation with logarithmic source terms , 2019, J. Intell. Fuzzy Syst..

[5]  Salah Boulaaras,et al.  L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem , 2011, Appl. Math. Comput..

[6]  Klaus Schmitt,et al.  Upper and Lower Solutions and Semilinear 2nd Order Elliptic-equations With Non-linear Boundary-conditions , 1985 .

[7]  M. Ruzicka,et al.  Electrorheological Fluids: Modeling and Mathematical Theory , 2000 .

[8]  Salah Boulaaras,et al.  A well-posedness and exponential decay of solutions for a coupled Lamé system with viscoelastic term and logarithmic source terms , 2019, Applicable Analysis.

[9]  G. Dragoni,et al.  II problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine , 1931 .

[10]  S. Boulaaras.  Existence of positive solutions for a new class of Kirchhoff parabolic systems , 2020 .

[11]  L. Erbe.  Nonlinear boundary value problems for second order differential equations , 1970 .

[12]  Giovany M. Figueiredo,et al.  On an elliptic equation of p-Kirchhoff type via variational methods , 2006, Bulletin of the Australian Mathematical Society.

[13]  S. Boulaaras,et al.  Existence of Positive Solutions for a Class of Quasilinear Singular Elliptic Systems Involving Caffarelli-Kohn-Nirenberg Exponent with Sign-Changing Weight Functions , 2018, Indian Journal of Pure and Applied Mathematics.

[14]  Biagio Ricceri,et al.  On an elliptic Kirchhoff-type problem depending on two parameters , 2008, J. Glob. Optim..

[15]  Jacques-Louis Lions,et al.  On Some Questions in Boundary Value Problems of Mathematical Physics , 1978 .

[16]  Klaus Schmitt,et al.  Periodic boundary value problems for systems of second order differential equations , 1973 .

[17]  K. Schmitt,et al.  Bifurcation problems associated with generalized Laplacians , 2004, Advances in Differential Equations.

[18]  The finite element approximation of evolutionary Hamilton–Jacobi–Bellman equations with nonlinear source terms , 2013 .

[19]  P. Clément,et al.  Existence and a Priori Estimates for Positive Solutions of p-Laplace Systems , 2002 .

[20]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[21]  Caisheng Chen,et al.  On positive weak solutions for a class of quasilinear elliptic systems , 2005 .

[22]  H. Knobloch,et al.  Eine neue Methode zur Approximation periodischer Lösungen nicht-linearer Differentialgleichungen zweiter Ordnung , 1963 .

[23]  S. Boulaaras,et al.  Existence of positive solutions for nonlocal p ⁢ ( x ) p(x) -Kirchhoff elliptic systems , 2019, Advances in Pure and Applied Mathematics.

[24]  S. Boulaaras,et al.  Blow-up of solutions for a system of nonlocal singular viscoelastic equations , 2018 .

[25]  P. Habets,et al.  Non-linear boundary value problems for systems of differential equations† , 1977, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[26]  S. Boulaaras,et al.  Existence of positive solutions for a new class of nonlocal p(x)-Kirchhoff elliptic systems via sub-super solutions concept , 2018 .

[27]  S. Boulaaras,et al.  Existence Of Positive Radial Solutions For ( p ( x ) , q ( x ) )-Laplacian Systems ∗ , 2018 .

[28]  Salah Boulaaras,et al.  Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation , 2018, Bulletin of the Malaysian Mathematical Sciences Society.

[29]  A. El Hamidi,et al.  Existence results to elliptic systems with nonstandard growth conditions , 2004 .

[30]  P. Górka,et al.  One-dimensional Klein–Gordon equation with logarithmic nonlinearities , 2008 .

[31]  Michel Chipot,et al.  Some remarks on non local elliptic and parabolic problems , 1997 .

[32]  Qihu Zhang,et al.  Existence of positive solutions for a class of p(x)-Laplacian systems ✩ , 2007 .

[33]  Yalçın Güldü,et al.  On integral representation for solution of generalized Sturm-Liouville equation with discontinuity conditions , 2014 .

[34]  K. Schmitt,et al.  Some general concepts of sub- and supersolutions for nonlinear elliptic problems , 2006 .

[35]  S. Boulaaras,et al.  An asymptotic behavior of positive solutions for a new class of elliptic systems involving of $$\left( p\left( x\right) ,q\left( x\right) \right) $$px,qx-Laplacian systems , 2019 .

[36]  J. García-Melián,et al.  Some counterexamples related to the stationary Kirchhoff equation , 2016 .

[37]  Salah Boulaaras,et al.  Existence of Positive Solutions of Nonlocal p(x)-Kirchhoff Evolutionary Systems via Sub-Super Solutions Concept , 2019, Symmetry.

[38]  V. Le.  Subsolution-supersolution method in variational inequalities , 2001 .

[39]  Qihu Zhang,et al.  A strong maximum principle for differential equations with nonstandard p(x)-growth conditions , 2005 .

[40]  Salah Boulaaras,et al.  Global existence of solutions to a viscoelastic non-degenerate Kirchhoff equation , 2018, Applicable Analysis.

[41]  E. N. Dancer,et al.  On the existence of a maximal weak solution for a semilinear elliptic equation , 1989, Differential and Integral Equations.

[42]  N. Azzouz,et al.  Existence Results for an Elliptic Equation of Kirchhoff-Type with Changing Sign Data , 2012 .

[43]  E. Massa,et al.  On necessary conditions for the comparison principle and the sub- and supersolution method for the stationary Kirchhoff equation , 2017, 1710.11061.

[44]  Khaled Zennir,et al.  Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System , 2019, Symmetry.

[45]  On the sub-supersolution method for p(x)-Kirchhoff type equations , 2012 .

[46]  D. D. Hai,et al.  An existence result on positive solutions for a class of p-Laplacian systems , 2004 .

[47]  Salah Boulaaras,et al.  Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity , 2019, Mathematical Methods in the Applied Sciences.

[48]  Klaus Schmitt,et al.  Periodic solutions of nonlinear second order differential equations , 1967 .

[49]  J. G. Azorero,et al.  Existence and nonuniqueness for the p-laplacian , 1987 .

[50]  Vicentiu D. Rădulescu,et al.  Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent , 2008 .

[51]  S. Boulaaras,et al.  General decay for a viscoelastic problem with not necessarily decreasing kernel , 2018 .

[52]  Herbert Amann,et al.  On Some Existence Theorems for Semi-Linear Elliptic Equations. , 1977 .

[53]  Salah Boulaaras,et al.  Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters , 2018 .

[54]  J. García Azorero,et al.  Existence and nonuniqueness for the p-Laplacian nonlinear Eigenvalues , 1987 .

[55]  S. Boulaaras,et al.  An asymptotic behavior of positive solutions for a new class of elliptic systems involving of ( p (x), q (x))-Laplacian systems , 2019 .

[56]  Otared Kavian,et al.  Introduction à la théorie des points critiques : et applications aux problèmes elliptiques , 1993 .

[57]  H. Lewy.  Erratum: An Example of a Smooth Linear Partial Differential Equation Without Solution , 1957 .