Sufficient conditions for the existence of heteroclinic solutions for -Laplacian differential equations

References

• Cupini G, Marcelli C, Papalini F. On the solvability of a boundary value problem on the real line. Boundary Value Prob. 2011;2011:26.
   Web of Science ®Google Scholar
• Marcelli C. The role of boundary data on the solvability of some equations involving non-autonomous nonlinear differential, operators. Boundary Value Prob. 2013;2013:252.
   Web of Science ®Google Scholar
• Bianconi B, Papalini F. Non-autonomous boundary value problems on the real line. Discr. Contin. Dyn. Syst. 2006;15:759–776.
   Web of Science ®Google Scholar
• Ferracuti L, Papalini F. Boundary value problems for strongly nonlinear multivalued equations involving different φ-Laplacians. Adv. Differ. Equ. 2009;14:541–566.
   Web of Science ®Google Scholar
• Gilding BH, Kersner R. Travelling waves in nonlinear diffusion--convection--reaction. Basel: Birkhäuser; 2004.
   Google Scholar
• Graef J, Kong L, Minh\’{o}s F. Higher order boundary value problems with φ-Laplacian and functional boundary conditions. Comput. Math. App. 2011;61:236–249.
   Web of Science ®Google Scholar
• Graef J, Kong L, Minh\’{o}s F, et al. On the lower and upper solutions method for higher order functional boundary value problems. Appl. Anal. Discr. Math. 2011;5:133–146.
   Web of Science ®Google Scholar
• Alves CO. Existence of heteroclinic solutions for a class of non-autonomous second-order equation. Nonlinear Differ. Equ. Appl. 2015;2:1195–1212.
   Web of Science ®Google Scholar
• Calamai A. Heteroclinic solutions of boundary value problems on the real line involving singular φ-Laplacian operators. J. Math. Anal. Appl. 2011;378:667–679.
   Web of Science ®Google Scholar
• Izydorek M, Janczewska J. Homoclinic solutions for a class of the second order Hamiltonian systems. J. Differ. Equ. 2005;219:375–389.
   Web of Science ®Google Scholar
• Liu Y. Existence of solutions of boundary value problems for coupled singular differential equations on whole lines with impulses. Mediterr. J. Math. 2015;12:697–716.
   Web of Science ®Google Scholar
• Marcelli C. Existence of solutions to boundary value problems governed by general non-autonomous nonlinear differential operators. Electron. J. Differ. Equ. 2012;2012:1–18.
   Web of Science ®Google Scholar
• Sun J, Chen H, Nieto JJ. Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. J. Math. Anal. Appl. 2011;373:20–29.
   Web of Science ®Google Scholar
• Tersian S, Chaparova J. Periodic and homoclinic solutions of extended Fisher--Kolmogorov equations. J. Math. Anal. Appl. 2001;260:490–506.
   Web of Science ®Google Scholar
• Wang J, Xu J, Zhang F. Homoclinic orbits for a class of Hamiltonian systems with superquadratic or asymptotically quadratic potentials. Commun. Pure Appl. Anal. 2011;10:269–286.
   Web of Science ®Google Scholar
• Arias M, Campos J, Marcelli C. Fastness and continuous dependence in front propagation in Fisher-KPP equations. Discr. Contin. Dyn. Syst., Ser. B. 2009;11:11–30.
   Web of Science ®Google Scholar
• Bereanu C, Mawhin J. Boundary-value problems with non-surjective φ-Laplacian and oneside bounded nonlinearity. Adv. Differ. Equ. 2006;11:35–60.
   Web of Science ®Google Scholar
• Cabada A, Ángel Cid J. Heteroclinic solutions for non-autonomous boundary value problems with singular φ-Laplacian operators. Discr. Contin. Dyn. Syst. Suppl: 2009, 118–122.
   Google Scholar
• Cabada A, Pouso RL. Existence results for the problem (φ(u')') = f(t,u,u') with nonlinear boundary conditions. Nonlinear Anal. 1999;35:221–231.
   Web of Science ®Google Scholar
• Fabry C, Manásevich R. Equations with a p-Laplacian and an asymmetric nonlinear term. Discr. Contin. Dyn. Syst. 2001;7:545–557.
   Web of Science ®Google Scholar
• Maini PK, Malaguti L, Marcelli C, et al. Diffusion-aggregation processes with mono-stable reaction terms. Discr. Cont. Dyn. Syst. (B). 2006;6:1175–1189.
   Web of Science ®Google Scholar
• Papageorgiou NS, Papalini F. Pairs of positive solutions for the periodic scalar p-Laplacian.\pagination{\break} J. Fixed Point Theory. 2009;5:157–184.
   Web of Science ®Google Scholar
• del Pino M, Elgueta M, Manásevich R. A homotopic deformation along p of a Leray--Schauder degree result and existence for (|u'|p-2u') + f(t,u) = 0,u(0) = u(t) = 0,p > 1. J. Differ. Equ. 1989;80:1–13.
   Web of Science ®Google Scholar
• Corduneanu C. Integral equations and stability of feedback systems. New York (NY): Academic Press; 1973.
   Google Scholar
• Zeidler E. Nonlinear functional analysis and its applications, I: fixed-point theorems.\pagination{\break} New York (NY): Springer; 1986.
   Google Scholar